A275090 -id:A275090

A275085

Number of n X 3 0..2 arrays with no element equal to any value at offset (0,-2) (-1,-2) or (-2,-1) and new values introduced in order 0..2.

+10
1

3, 36, 192, 1024, 5440, 29120, 155904, 834176, 4463424, 23883904, 127801600, 683853952, 3659249536, 19580378368, 104773120768, 560632993280, 2999904734464, 16052263263232, 85894445131264, 459614672161280

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 4*a(n-1) + 4*a(n-2) + 14*a(n-3) + 18*a(n-4) - 8*a(n-5) + 16*a(n-6) + 80*a(n-7) - 32*a(n-8) - 64*a(n-9) for n>10.

Empirical g.f.: x*(3 + 24*x + 36*x^2 + 70*x^3 + 18*x^4 - 48*x^5 + 112*x^6 + 208*x^7 - 160*x^8 - 192*x^9) / (1 - 4*x - 4*x^2 - 14*x^3 - 18*x^4 + 8*x^5 - 16*x^6 - 80*x^7 + 32*x^8 + 64*x^9). - Colin Barker, Jan 31 2019

EXAMPLE

Some solutions for n=4:

..0..1..2. .0..0..1. .0..1..1. .0..0..1. .0..0..1. .0..0..1. .0..0..1

..2..2..1. .0..0..2. .1..1..2. .0..0..1. .0..1..2. .1..0..2. .2..0..1

..2..2..0. .2..2..1. .1..1..0. .0..1..1. .2..1..1. .1..2..2. .0..2..1

..0..1..1. .0..2..1. .2..0..0. .1..2..2. .1..1..0. .1..0..2. .1..1..2

CROSSREFS

Column 3 of A275090.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 16 2016

STATUS

approved

A275086

Number of nX4 0..2 arrays with no element equal to any value at offset (0,-2) (-1,-2) or (-2,-1) and new values introduced in order 0..2.

+10
1

6, 96, 508, 3088, 18440, 111900, 675600, 4094240, 24794560, 150165020, 909361668, 5507667148, 33356744732, 202019640344, 1223500857956, 7410005643024, 44877800876060, 271796556988084, 1646101595999968, 9969411699754184

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Column 4 of A275090.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 3*a(n-1) +8*a(n-2) +46*a(n-3) +133*a(n-4) -64*a(n-5) -492*a(n-6) -520*a(n-7) +568*a(n-8) -1592*a(n-9) +1156*a(n-10) +1328*a(n-11) -4992*a(n-12) +1440*a(n-13) +3456*a(n-14) for n>15

EXAMPLE

Some solutions for n=4

..0..0..1..2. .0..0..1..2. .0..1..1..2. .0..1..1..0. .0..0..1..1

..0..0..1..1. .0..2..1..1. .0..1..1..0. .0..1..1..2. .1..0..2..1

..0..1..2..2. .0..1..1..0. .1..1..2..2. .1..1..2..2. .1..1..2..2

..0..1..1..0. .2..1..1..0. .2..2..0..0. .1..1..2..0. .0..2..2..0

CROSSREFS

Cf. A275090.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 16 2016

STATUS

approved

A275087

Number of nX5 0..2 arrays with no element equal to any value at offset (0,-2) (-1,-2) or (-2,-1) and new values introduced in order 0..2.

+10
1

12, 288, 1680, 12816, 87924, 647648, 4706400, 34281472, 248629316, 1807849760, 13148091944, 95586744116, 694768673948, 5050803706792, 36719738878324, 266942014046252, 1940565298670908, 14107383564812316, 102557258518158564

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Column 5 of A275090.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 2*a(n-1) +15*a(n-2) +101*a(n-3) +450*a(n-4) +587*a(n-5) -948*a(n-6) -6010*a(n-7) -692*a(n-8) +18832*a(n-9) -31839*a(n-10) +1958*a(n-11) +58620*a(n-12) -170990*a(n-13) +243302*a(n-14) -278201*a(n-15) +182523*a(n-16) +57164*a(n-17) -121679*a(n-18) +9439*a(n-19) +37154*a(n-20) +841*a(n-21) -863*a(n-22) +182*a(n-23) +60*a(n-24) -6*a(n-25) -2*a(n-26) +a(n-27) for n>28

EXAMPLE

Some solutions for n=4

..0..0..1..1..0. .0..1..2..2..0. .0..1..1..0..2. .0..1..2..0..0

..0..1..1..2..0. .1..1..2..0..0. .1..1..2..0..0. .1..1..2..0..1

..1..1..2..2..0. .1..2..2..0..0. .1..2..2..0..1. .1..2..0..0..1

..0..2..2..0..1. .0..0..2..1..1. .1..2..0..0..1. .2..0..0..1..1

CROSSREFS

Cf. A275090.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 16 2016

STATUS

approved

A275088

Number of nX6 0..2 arrays with no element equal to any value at offset (0,-2) (-1,-2) or (-2,-1) and new values introduced in order 0..2.

+10
1

24, 864, 5304, 53132, 510680, 5038428, 48675088, 477786368, 4669603380, 45596095332, 445618877780, 4354996501396, 42558814118692, 415901491499748, 4064202093487220, 39716691445365360, 388129218814938872

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Column 6 of A275090.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

R. H. Hardin, Empirical recurrence of order 64

FORMULA

Empirical recurrence of order 64 (see link above)

EXAMPLE

Some solutions for n=4

..0..0..1..1..2..0. .0..1..2..2..1..1. .0..1..1..2..2..1. .0..0..1..1..2..0

..0..1..1..2..2..0. .1..0..2..2..1..0. .0..1..1..2..0..0. .2..0..1..2..2..0

..0..1..1..2..0..1. .1..2..2..1..0..0. .0..1..2..0..0..1. .0..1..1..2..2..0

..1..2..2..0..0..1. .1..0..2..1..0..2. .1..2..2..0..1..2. .0..0..2..2..0..0

CROSSREFS

Cf. A275090.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 16 2016

STATUS

approved

A275089

Number of nX7 0..2 arrays with no element equal to any value at offset (0,-2) (-1,-2) or (-2,-1) and new values introduced in order 0..2.

+10
1

48, 2592, 17184, 232156, 2934756, 38872396, 512150588, 6767371752, 89090043684, 1174911360788, 15503814279976, 204476407498760, 2696824987632772, 35568778483055352, 469145522114492964, 6187939649650112040

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Column 7 of A275090.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..133

EXAMPLE

Some solutions for n=3

..0..0..1..1..2..2..1. .0..1..2..2..0..0..2. .0..0..1..2..0..1..2

..2..1..1..2..2..0..1. .0..1..2..0..0..1..1. .0..2..2..1..0..0..2

..0..1..1..0..2..1..1. .0..1..2..0..0..2..2. .1..2..2..0..1..2..2

CROSSREFS

Cf. A275090.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 16 2016

STATUS

approved

A275091

Number of 3Xn 0..2 arrays with no element equal to any value at offset (0,-2) (-1,-2) or (-2,-1) and new values introduced in order 0..2.

+10
1

5, 81, 192, 508, 1680, 5304, 17184, 54484, 176736, 566532, 1831420, 5898428, 19030840, 61351112, 197821048, 637917924, 2056541796, 6631985064, 21381565940, 68947715488, 222300888872, 716808527616, 2311205195976, 7452291640756

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Row 3 of A275090.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 2*a(n-1) +9*a(n-2) -10*a(n-3) -30*a(n-4) +3*a(n-5) +90*a(n-6) +117*a(n-7) -366*a(n-8) -129*a(n-9) +477*a(n-10) -102*a(n-11) -166*a(n-12) +659*a(n-13) +144*a(n-14) -1305*a(n-15) -317*a(n-16) +1101*a(n-17) +9*a(n-18) -613*a(n-19) +657*a(n-20) -96*a(n-21) -422*a(n-22) +72*a(n-23) +167*a(n-24) +295*a(n-25) -252*a(n-26) -148*a(n-27) +133*a(n-28) +33*a(n-29) +19*a(n-30) -39*a(n-31) +8*a(n-33) +2*a(n-34) -a(n-36) for n>38

EXAMPLE

Some solutions for n=4

..0..1..1..0. .0..1..2..0. .0..0..1..2. .0..0..1..2. .0..1..2..2

..2..1..1..0. .0..1..1..0. .0..1..1..2. .2..2..1..1. .0..1..1..2

..2..1..0..0. .1..2..2..0. .2..1..1..0. .2..1..1..0. .1..2..2..0

CROSSREFS

Cf. A275090.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 16 2016

STATUS

approved

A275092

Number of 4Xn 0..2 arrays with no element equal to any value at offset (0,-2) (-1,-2) or (-2,-1) and new values introduced in order 0..2.

+10
1

14, 486, 1024, 3088, 12816, 53132, 232156, 984288, 4304608, 18686420, 81545856, 355534620, 1548803468, 6754327372, 29407955624, 128203071808, 558360538308, 2433519428172, 10601710686752, 46199290950200, 201293175872408

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Row 4 of A275090.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

R. H. Hardin, Empirical recurrence of order 84

FORMULA

Empirical recurrence of order 84 (see link above)

EXAMPLE

Some solutions for n=4

..0..1..1..2. .0..1..1..2. .0..1..2..0. .0..0..1..2. .0..1..2..0

..1..1..2..0. .1..1..2..2. .2..1..1..0. .1..0..2..1. .0..2..2..0

..1..1..2..0. .1..1..0..0. .1..1..0..0. .0..1..2..2. .0..1..2..0

..1..2..2..0. .0..2..2..0. .1..1..2..2. .0..2..2..0. .0..2..1..0

CROSSREFS

Cf. A275090.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 16 2016

STATUS

approved

A275093

Number of 5Xn 0..2 arrays with no element equal to any value at offset (0,-2) (-1,-2) or (-2,-1) and new values introduced in order 0..2.

+10
1

41, 2916, 5440, 18440, 87924, 510680, 2934756, 16976416, 100163280, 587376672, 3441832776, 20278827840, 119081922956, 699883834544, 4115716304856, 24201876220300, 142224779364880, 836403191956404, 4917486759591212

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Row 5 of A275090.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

EXAMPLE

Some solutions for n=4

..0..1..1..2. .0..0..1..2. .0..0..1..2. .0..1..1..2. .0..1..2..0

..1..1..2..2. .0..2..2..1. .0..2..1..1. .0..1..1..0. .1..1..2..0

..1..1..0..0. .0..2..2..0. .2..1..1..0. .0..1..2..2. .0..1..2..0

..1..2..2..0. .0..2..1..1. .0..1..1..0. .1..2..2..0. .1..2..2..0

..1..0..2..1. .0..2..1..0. .0..1..2..2. .0..1..2..0. .1..2..0..1

CROSSREFS

Cf. A275090.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 16 2016

STATUS

approved

A275094

Number of 6Xn 0..2 arrays with no element equal to any value at offset (0,-2) (-1,-2) or (-2,-1) and new values introduced in order 0..2.

+10
1

122, 17496, 29120, 111900, 647648, 5038428, 38872396, 303675960, 2423227760, 19202061888, 152553328244, 1215089208420, 9668080103560, 76882965502680, 612018920913868, 4870269177219740, 38747349177636904, 308437956528230860

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Row 6 of A275090.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..171

EXAMPLE

Some solutions for n=4

..0..0..1..2. .0..1..1..0. .0..1..1..0. .0..1..1..2. .0..1..1..0

..1..2..2..1. .0..1..1..2. .1..1..2..2. .0..2..1..0. .2..2..1..0

..1..2..2..0. .0..1..2..2. .2..2..0..0. .0..2..2..0. .2..1..0..0

..2..0..0..1. .1..2..2..0. .2..2..0..1. .2..2..1..0. .1..0..0..2

..1..0..0..1. .1..2..2..0. .2..0..0..1. .2..2..1..0. .0..0..2..2

..1..0..2..1. .2..0..0..1. .1..0..0..1. .2..1..1..0. .0..0..1..2

CROSSREFS

Cf. A275090.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 16 2016

STATUS

approved

A275095

Number of 7 X n 0..2 arrays with no element equal to any value at offset (0,-2) (-1,-2) or (-2,-1) and new values introduced in order 0..2.

+10
1

365, 104976, 155904, 675600, 4706400, 48675088, 512150588, 5409118916, 58485063272, 627063902032, 6757273029432, 72848042422536, 785795946135408, 8476340619088292, 91452795188833412, 986763165449841128

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Row 7 of A275090.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..73

EXAMPLE

Some solutions for n=3

..0..1..1. .0..1..1. .0..1..1. .0..0..1. .0..0..1. .0..0..1. .0..0..1

..1..2..2. .0..1..2. .1..0..2. .0..1..1. .2..0..1. .1..1..2. .0..0..2

..1..2..0. .1..2..2. .2..2..0. .0..1..2. .2..2..1. .0..1..2. .0..2..2

..2..2..0. .1..1..0. .0..2..1. .1..1..2. .0..0..1. .1..2..2. .0..2..1

..2..2..1. .1..0..0. .2..1..1. .1..1..2. .2..1..1. .0..2..2. .2..1..1

..1..0..0. .2..0..0. .1..2..0. .1..0..0. .0..1..1. .2..0..1. .2..1..0

..1..0..0. .0..2..1. .1..1..2. .1..2..2. .1..0..2. .0..1..1. .1..0..0

CROSSREFS

Cf. A275090.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 16 2016

STATUS

approved