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A295115 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s. 1

%I

%S 3,9,26,77,226,665,1960,5769,16983,49998,147198,433361,1275825,

%T 3756068,11058011,32555211,95843749,282167522,830711657,2445646047,

%U 7200072866,21197281911,62405585330,183724361820,540891347189,1592404221036

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

%H R. H. Hardin, <a href="/A295115/b295115.txt">Table of n, a(n) for n = 1..210</a>

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

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

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 3 of A295120.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 15 2017

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Last modified May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)