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A295374 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2 or 4 1s. 1

%I #8 Feb 22 2019 09:55:00

%S 5,19,74,278,1067,4071,15557,59407,226944,866828,3311093,12647369,

%T 48309585,184528995,704849914,2692330642,10283957167,39281862695,

%U 150045822457,573133422103,2189210714608,8362177726832,31941199613977

%N Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2 or 4 1s.

%H R. H. Hardin, <a href="/A295374/b295374.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 4*a(n-2) - 3*a(n-3) + a(n-4) - 8*a(n-5) - 3*a(n-6) + 5*a(n-7) - 2*a(n-8) + a(n-9) + a(n-10).

%F Empirical g.f.: x*(5 + 4*x - 3*x^2 - 5*x^3 - 11*x^4 + x^5 + 3*x^6 - x^7 + 2*x^8 + x^9) / (1 - 3*x - 4*x^2 + 3*x^3 - x^4 + 8*x^5 + 3*x^6 - 5*x^7 + 2*x^8 - x^9 - x^10). - _Colin Barker_, Feb 22 2019

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 3 of A295379.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 21 2017

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Last modified February 23 06:06 EST 2024. Contains 370267 sequences. (Running on oeis4.)