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R. H. Hardin, <a href="/A304923/b304923.txt">Table of n, a(n) for n = 1..210</a>

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Number of nX5 0..1 arrays with every element unequal to 0, 1, 2, 5 or 7 king-move adjacent elements, with upper left element zero.

16, 22, 73, 266, 1054, 4186, 16158, 63555, 251536, 988178, 3881249, 15283765, 60169598, 236666582, 931151693, 3664515375, 14419463010, 56735373146, 223247607871, 878464272129, 3456612805830, 13601219460000, 53519079374945

1,1

Column 5 of A304926.

Empirical: a(n) = 3*a(n-1) +3*a(n-2) +15*a(n-3) -21*a(n-4) -101*a(n-5) -119*a(n-6) +168*a(n-7) +750*a(n-8) +338*a(n-9) -1047*a(n-10) -1984*a(n-11) -170*a(n-12) +2290*a(n-13) +3270*a(n-14) -457*a(n-15) -3277*a(n-16) -3185*a(n-17) +659*a(n-18) +2939*a(n-19) +2559*a(n-20) -532*a(n-21) -2150*a(n-22) -1076*a(n-23) +37*a(n-24) +823*a(n-25) +638*a(n-26) -122*a(n-27) -97*a(n-28) -116*a(n-29) -96*a(n-30) +59*a(n-31) -2*a(n-32) -8*a(n-33) +10*a(n-34) for n>41

Some solutions for n=5

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

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

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

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

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

Cf. A304926.

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R. H. Hardin, May 21 2018

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