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Number of nX3 0..1 arrays with every element equal to 1, 2, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
1

%I #4 Apr 09 2018 09:20:42

%S 1,7,28,115,497,2086,9091,40575,172996,760155,3348129,14520438,

%T 63606819,278902951,1216232548,5321761651,23294489377,101772095142,

%U 445140686771,1947282645119,8512898474820,37229821964539,162827989419377

%N Number of nX3 0..1 arrays with every element equal to 1, 2, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%C Column 3 of A302528.

%H R. H. Hardin, <a href="/A302523/b302523.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +7*a(n-2) +34*a(n-3) -44*a(n-4) -182*a(n-5) -a(n-6) +54*a(n-7) +479*a(n-8) -772*a(n-9) +328*a(n-10) +2176*a(n-11) -1456*a(n-12) +1088*a(n-13) -4480*a(n-14) +5120*a(n-15) -2304*a(n-16) -5120*a(n-17) +4096*a(n-18)

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A302528.

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 09 2018