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A295046 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 0 or 2 1s. 1

%I #9 Feb 22 2019 06:03:06

%S 5,19,72,270,1027,3879,14691,55589,210418,796360,3014159,11408021,

%T 43177713,163420621,618521718,2341006856,8860343731,33535006265,

%U 126924727467,480390130557,1818201106700,6881605261574,26045793772285

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

%H R. H. Hardin, <a href="/A295046/b295046.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) - 2*a(n-4) - 6*a(n-5) + 3*a(n-6) - a(n-7) + a(n-9).

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

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 3 of A295051.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 13 2017

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Last modified April 14 12:23 EDT 2024. Contains 371661 sequences. (Running on oeis4.)