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A283410 Number of n X 3 0..1 arrays with no 1 equal to more than three of its horizontal, vertical and antidiagonal neighbors. 1

%I #7 Feb 21 2019 08:19:11

%S 8,61,416,2944,20744,146228,1030788,7266120,51219756,361053936,

%T 2545110952,17940781184,126466639652,891477956620,6284131129240,

%U 44297566481868,312258664857680,2201147411081008,15516142450416040

%N Number of n X 3 0..1 arrays with no 1 equal to more than three of its horizontal, vertical and antidiagonal neighbors.

%H R. H. Hardin, <a href="/A283410/b283410.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) + 13*a(n-2) + 10*a(n-3) + a(n-4) + 2*a(n-5) for n>7.

%F Empirical g.f.: x*(1 + x)*(8 + 13*x - 6*x^2 - 3*x^3 + x^4 - 2*x^5) / (1 - 5*x - 13*x^2 - 10*x^3 - x^4 - 2*x^5). - _Colin Barker_, Feb 21 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 3 of A283415.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 07 2017

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)