A298230 -id:A298230

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A298225

Number of nX3 0..1 arrays with every element equal to 0, 1, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

+10
1

3, 4, 5, 17, 12, 100, 219, 498, 1999, 4953, 13928, 45164, 120865, 355474, 1065723, 2987665, 8792232, 25703174, 73648001, 215508142, 625811209, 1809121989, 5271819208, 15292192284, 44347119815, 128947618162, 374125557341

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

OFFSET

1,1

COMMENTS

Column 3 of A298230.

LINKS

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

FORMULA

Empirical: a(n) = a(n-1) +4*a(n-2) +13*a(n-3) -14*a(n-4) -29*a(n-5) -23*a(n-6) +29*a(n-7) +56*a(n-8) -30*a(n-9) -7*a(n-10) +41*a(n-11) +2*a(n-12) -26*a(n-13) -12*a(n-14) -15*a(n-15) -7*a(n-16) +16*a(n-17) +2*a(n-18) for n>19

EXAMPLE

Some solutions for n=7

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

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

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

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

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

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

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

CROSSREFS

Cf. A298230.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 15 2018

STATUS

approved

A298226

Number of nX4 0..1 arrays with every element equal to 0, 1, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

+10
1

5, 16, 17, 195, 490, 2606, 15646, 74688, 397909, 2172360, 11380566, 60631430, 325152997, 1728286947, 9215894735, 49218645591, 262327473375, 1399145008769, 7465029674488, 39810676235989, 212342781125559, 1132682956110103

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

OFFSET

1,1

COMMENTS

Column 4 of A298230.

LINKS

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

FORMULA

Empirical: a(n) = 4*a(n-1) +7*a(n-2) +53*a(n-3) -232*a(n-4) -308*a(n-5) -590*a(n-6) +4313*a(n-7) +3326*a(n-8) -275*a(n-9) -33661*a(n-10) -3750*a(n-11) +34619*a(n-12) +97423*a(n-13) -102142*a(n-14) -129702*a(n-15) +42710*a(n-16) +453288*a(n-17) -191477*a(n-18) -553360*a(n-19) -215979*a(n-20) +1609482*a(n-21) -195851*a(n-22) -2386398*a(n-23) -546805*a(n-24) +4132384*a(n-25) +1003867*a(n-26) -7275172*a(n-27) -207426*a(n-28) +9905631*a(n-29) +3119003*a(n-30) -10615571*a(n-31) -5141402*a(n-32) +8332419*a(n-33) +8109079*a(n-34) -3922996*a(n-35) -10219033*a(n-36) -7778489*a(n-37) +4353156*a(n-38) +5882154*a(n-39) -2124795*a(n-40) -9254272*a(n-41) +159018*a(n-42) +4829413*a(n-43) +7423302*a(n-44) +7099748*a(n-45) +12036958*a(n-46) +7705063*a(n-47) -1434288*a(n-48) -13492716*a(n-49) -11913233*a(n-50) -4219196*a(n-51) +2931767*a(n-52) +3319849*a(n-53) +645459*a(n-54) -167241*a(n-55) +152274*a(n-56) +1027296*a(n-57) +441490*a(n-58) -53356*a(n-59) -306724*a(n-60) -139701*a(n-61) -13875*a(n-62) +12538*a(n-63) +10063*a(n-64) -527*a(n-65) -84*a(n-66) for n>68

EXAMPLE

Some solutions for n=7

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

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

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

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

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

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

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

CROSSREFS

Cf. A298230.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 15 2018

STATUS

approved

A298227

Number of nX5 0..1 arrays with every element equal to 0, 1, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

+10
1

8, 50, 12, 490, 1749, 7038, 71212, 440402, 2785299, 22451954, 156085555, 1080413616, 8143080250, 58022725348, 413685226967, 3035994512259, 21816461282403, 157007597256407, 1140825200514746, 8225611070991142

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

OFFSET

1,1

COMMENTS

Column 5 of A298230.

LINKS

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

EXAMPLE

Some solutions for n=7

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

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

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

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

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

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

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

CROSSREFS

Cf. A298230.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 15 2018

STATUS

approved

A298228

Number of nX6 0..1 arrays with every element equal to 0, 1, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

+10
1

13, 112, 100, 2606, 7038, 110320, 1166270, 10448313, 136604409, 1503351175, 16286627637, 194230966568, 2198476953879, 24700789917927, 286624459000212, 3264613409193272, 37095755700798148, 426284736792747449

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

OFFSET

1,1

COMMENTS

Column 6 of A298230.

LINKS

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

EXAMPLE

Some solutions for n=6

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

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

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

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

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

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

CROSSREFS

Cf. A298230.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 15 2018

STATUS

approved

A298229

Number of nX7 0..1 arrays with every element equal to 0, 1, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

+10
1

21, 348, 219, 15646, 71212, 1166270, 25406586, 353699661, 6688607300, 128037046425, 2233455463049, 41229191798129, 775524676522648, 14045073377885063, 259265856410756757, 4817848310541414512

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

OFFSET

1,1

COMMENTS

Column 7 of A298230.

LINKS

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

EXAMPLE

Some solutions for n=5

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

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

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

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

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

CROSSREFS

Cf. A298230.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 15 2018

STATUS

approved

A298224

Number of n X n 0..1 arrays with every element equal to 0, 1, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

+10
0

1, 4, 5, 195, 1749, 110320, 25406586, 7311722995, 11308912804354

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

OFFSET

1,2

COMMENTS

Diagonal of A298230.

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

Some solutions for n=6

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

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

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

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

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

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

CROSSREFS

Cf. A298230.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 15 2018

STATUS

approved

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