cp's OEIS Frontend

A295208 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1's.

%I A295208 #9 Apr 20 2021 15:15:12
%S A295208 1,4,10,27,102,345,1162,4072,14224,49604,173594,607485,2125150,
%T A295208 7436416,26022865,91060814,318652127,1115077417,3902040209,
%U A295208 13654599697,47782246634,167206840944,585115414586,2047524354146,7165006769433
%N A295208 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1's.
%C A295208 Column 3 of A295213.
%H A295208 R. H. Hardin, <a href="/A295208/b295208.txt">Table of n, a(n) for n = 1..210</a>
%H A295208 Robert Israel, <a href="/A295208/a295208.pdf">Maple-assisted proof of formula</a>
%F A295208 Empirical: a(n) = 5*a(n-1) -7*a(n-2) +10*a(n-3) -18*a(n-4) +18*a(n-5) -5*a(n-6) -15*a(n-7) +7*a(n-8) -9*a(n-9) +10*a(n-10) -2*a(n-11) +a(n-12).
%F A295208 Empirical formula confirmed by _Robert Israel_, Nov 17 2017 (see link).
%e A295208 Some solutions for n=7
%e A295208 ..1..1..1. .0..1..1. .0..1..1. .1..1..1. .0..1..1. .0..1..1. .1..1..0
%e A295208 ..1..1..1. .0..1..1. .0..1..1. .1..0..1. .0..1..1. .0..1..1. .1..1..0
%e A295208 ..1..0..1. .0..0..0. .0..1..0. .1..1..1. .0..1..1. .1..1..1. .1..0..0
%e A295208 ..1..0..1. .1..1..0. .0..1..0. .1..1..0. .0..0..0. .1..0..1. .1..0..0
%e A295208 ..1..1..1. .1..1..0. .1..1..0. .0..0..0. .0..0..0. .1..0..1. .1..1..0
%e A295208 ..0..1..1. .1..1..0. .1..1..0. .1..1..1. .0..1..1. .1..1..1. .1..1..0
%e A295208 ..0..0..0. .0..0..0. .1..1..0. .1..1..1. .0..1..1. .0..1..1. .0..0..0
%Y A295208 Cf. A295213.
%K A295208 nonn
%O A295208 1,2
%A A295208 _R. H. Hardin_, Nov 17 2017