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

%I #6 Jun 10 2023 13:14:51

%S 8,35,154,692,3048,13712,61536,277248,1248512,5627072,25357376,

%T 114292352,515113792,2321755072,10464487552,47166021056,212586287680,

%U 958175791232,4318696862016,19465338739648,87734436661888,395438540064704

%N Number of n X 5 0..1 arrays with every element equal to 0, 1, 3 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

%C Column 5 of A302081.

%H R. H. Hardin, <a href="/A302078/b302078.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +17*a(n-2) -38*a(n-3) -68*a(n-4) +136*a(n-5) +64*a(n-6) -128*a(n-7) for n>9.

%e Some solutions for n=5

%e ..0..1..0..1..0. .0..1..1..1..0. .0..1..0..1..0. .0..1..0..1..0

%e ..0..1..1..1..0. .0..1..0..1..1. .0..0..1..1..0. .0..1..1..0..0

%e ..0..1..0..1..1. .0..0..0..0..1. .0..1..0..1..0. .0..1..0..1..0

%e ..0..1..0..0..1. .1..0..1..0..1. .0..0..0..1..0. .0..1..0..1..0

%e ..0..1..1..0..0. .1..1..1..0..0. .0..1..0..0..0. .0..1..1..1..0

%Y Cf. A302081.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 31 2018