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Search: a317823 -id:a317823
Displaying 1-7 of 7 results found.
page 1
     Sort: relevance | references | number | modified | created      Format: long | short | data
A317817
Number of nX2 0..1 arrays with every element unequal to 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
+10
3
1, 5, 16, 50, 160, 511, 1634, 5226, 16716, 53471, 171045, 547149, 1750258, 5598852, 17910021, 57291907, 183269625, 586256561, 1875361283, 5999045795, 19190195958, 61387032829, 196369427849, 628161199864, 2009408986694, 6427847623748
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 2 of A317823.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 3*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6)
EXAMPLE
Some solutions for n=5
..0..1. .0..1. .0..0. .0..1. .0..1. .0..0. .0..1. .0..0. .0..1. .0..1
..0..1. .0..0. .1..1. .0..1. .1..1. .1..1. .0..1. .1..0. .1..0. .1..1
..1..1. .1..0. .0..0. .0..0. .0..0. .0..1. .0..0. .1..0. .1..0. .1..0
..0..0. .1..0. .1..1. .1..1. .1..1. .0..0. .0..1. .0..0. .1..0. .0..1
..1..0. .1..0. .0..0. .0..1. .0..1. .0..1. .1..0. .0..1. .1..1. .0..1
CROSSREFS
Cf. A317823.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 07 2018
STATUS
approved
A317818
Number of nX3 0..1 arrays with every element unequal to 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
+10
1
1, 16, 35, 135, 356, 1113, 3150, 9484, 27522, 81798, 239572, 707803, 2080838, 6134691, 18056895, 53200116, 156648460, 461423021, 1358857346, 4002288009, 11787108436, 34715792064, 102243257032, 301126862896, 886870040361
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 3 of A317823.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = a(n-1) +7*a(n-2) +2*a(n-3) -10*a(n-4) -14*a(n-5) -16*a(n-6) -25*a(n-7) +36*a(n-8) +42*a(n-9) -26*a(n-10) +62*a(n-11) +10*a(n-12) -28*a(n-13) +20*a(n-14) -16*a(n-15) +4*a(n-16) for n>18
EXAMPLE
Some solutions for n=5
..0..1..1. .0..1..1. .0..1..0. .0..0..1. .0..0..1. .0..1..0. .0..0..0
..1..0..0. .1..0..0. .1..0..0. .1..0..0. .1..0..0. .1..0..1. .1..1..1
..0..0..1. .0..0..1. .0..1..1. .1..0..0. .1..0..1. .0..0..1. .0..1..1
..1..1..1. .0..1..0. .1..1..0. .0..0..1. .0..1..1. .0..0..1. .0..1..0
..0..0..0. .1..1..0. .0..0..1. .0..1..0. .1..0..0. .1..0..0. .0..1..0
CROSSREFS
Cf. A317823.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 07 2018
STATUS
approved
A317819
Number of nX4 0..1 arrays with every element unequal to 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
+10
1
2, 50, 135, 702, 2726, 11768, 48526, 203049, 846901, 3533862, 14751288, 61572336, 256988741, 1072703816, 4477368403, 18688452762, 78005403965, 325591740543, 1359014862402, 5672494506043, 23676864307080, 98826717050870
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 4 of A317823.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = a(n-1) +20*a(n-2) +6*a(n-3) -154*a(n-4) -117*a(n-5) +672*a(n-6) +587*a(n-7) -2050*a(n-8) -1804*a(n-9) +3999*a(n-10) +3942*a(n-11) -2519*a(n-12) -5840*a(n-13) -9009*a(n-14) +8051*a(n-15) +33470*a(n-16) -7813*a(n-17) -52983*a(n-18) -121*a(n-19) +41444*a(n-20) +12853*a(n-21) -6529*a(n-22) -19825*a(n-23) -19439*a(n-24) +13134*a(n-25) +21223*a(n-26) -2212*a(n-27) -10933*a(n-28) -1301*a(n-29) +3458*a(n-30) +557*a(n-31) -769*a(n-32) -110*a(n-33) +103*a(n-34) +19*a(n-35) -11*a(n-36) +a(n-37) for n>43
EXAMPLE
Some solutions for n=5
..0..1..0..1. .0..1..0..0. .0..1..1..0. .0..1..1..0. .0..1..1..1
..1..0..0..1. .1..1..1..0. .0..1..1..0. .0..1..0..0. .1..1..0..0
..0..0..0..0. .1..1..1..0. .0..1..1..1. .1..0..0..1. .0..0..0..0
..1..0..0..1. .0..1..1..0. .1..1..1..1. .0..0..0..1. .0..0..1..1
..1..1..1..0. .0..0..1..1. .0..0..0..1. .1..0..0..1. .1..1..1..0
CROSSREFS
Cf. A317823.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 07 2018
STATUS
approved
A317820
Number of nX5 0..1 arrays with every element unequal to 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
+10
1
3, 160, 356, 2726, 8556, 47374, 179111, 878802, 3604079, 16657873, 71153802, 320111818, 1390832362, 6188854830, 27092156914, 119925512941, 526911251983, 2326470845881, 10239421120031, 45158496956400, 198899068210330
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 5 of A317823.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 94
FORMULA
Empirical recurrence of order 94 (see link above)
EXAMPLE
Some solutions for n=5
..0..0..1..1..0. .0..1..0..1..0. .0..1..0..0..1. .0..1..0..0..1
..1..1..1..1..0. .1..0..0..1..1. .1..0..0..1..0. .0..1..1..1..1
..0..0..0..1..1. .0..0..1..1..0. .1..0..1..1..0. .1..1..0..0..1
..1..0..0..1..1. .1..1..1..0..1. .1..0..1..1..1. .0..0..0..0..1
..1..0..0..0..0. .1..0..0..0..1. .0..0..0..0..0. .1..1..0..0..0
CROSSREFS
Cf. A317823.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 07 2018
STATUS
approved
A317821
Number of nX6 0..1 arrays with every element unequal to 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
+10
1
5, 511, 1113, 11768, 47374, 296968, 1458418, 8231398, 43470698, 234869539, 1268932863, 6796211640, 36769146540, 197424396019, 1064758694845, 5732008854125, 30865744562047, 166276190963313, 895264358908034
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 6 of A317823.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=5
..0..0..1..1..0..1. .0..0..0..1..0..1. .0..0..0..1..1..0. .0..1..1..0..1..1
..1..0..0..0..1..1. .1..1..1..1..0..1. .1..0..0..0..0..1. .1..1..0..1..1..0
..1..0..0..1..1..0. .0..1..1..0..0..0. .1..0..0..0..1..0. .1..0..0..1..1..0
..0..0..0..1..1..0. .0..1..0..0..0..0. .0..1..1..1..1..0. .0..0..0..1..0..0
..1..1..0..0..1..0. .0..1..0..1..1..0. .1..1..0..0..1..0. .1..0..1..0..0..1
CROSSREFS
Cf. A317823.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 07 2018
STATUS
approved
A317822
Number of nX7 0..1 arrays with every element unequal to 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
+10
1
8, 1634, 3150, 48526, 179111, 1458418, 7370716, 49813114, 285365386, 1801862295, 10780737885, 66250927857, 402362478261, 2454261649360, 14947185490935, 91152367042211, 554926695836229, 3385228443629637, 20612211780845789
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 7 of A317823.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
EXAMPLE
Some solutions for n=5
..0..1..1..0..1..0..0. .0..1..1..1..0..0..1. .0..1..0..1..0..0..1
..1..1..0..1..1..0..1. .0..1..0..0..0..1..0. .1..0..0..1..1..1..1
..0..0..0..1..0..0..1. .1..0..0..0..1..1..0. .0..0..1..1..0..0..0
..0..0..1..1..0..0..0. .1..0..1..1..1..0..0. .0..1..1..0..0..0..0
..1..0..1..0..0..1..1. .0..1..1..0..0..0..1. .0..1..1..0..1..1..1
CROSSREFS
Cf. A317823.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 07 2018
STATUS
approved
A317816
Number of nXn 0..1 arrays with every element unequal to 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
+10
0
0, 5, 35, 702, 8556, 296968, 7370716, 384248160, 21424520640, 1842317433367, 222676829507057, 36099873530494859, 9133843424563202164
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Diagonal of A317823.
LINKS
Table of n, a(n) for n=1..13.
EXAMPLE
Some solutions for n=5
..0..1..1..1..1. .0..1..0..1..1. .0..1..0..0..1. .0..1..0..1..0
..0..0..0..0..0. .1..0..0..0..0. .1..1..1..0..0. .1..0..0..1..1
..1..0..0..1..1. .1..0..0..1..1. .0..1..1..0..0. .0..0..1..1..0
..1..0..1..1..0. .1..1..1..1..0. .0..1..1..0..1. .1..1..1..0..0
..0..0..1..0..1. .0..1..1..0..1. .0..0..1..0..1. .0..1..0..1..1
CROSSREFS
Cf. A317823.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 07 2018
STATUS
approved
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