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 A231377 Number of n X 3 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors. 1

%I #8 Sep 28 2018 15:19:15

%S 4,21,93,378,1519,6126,24747,99964,403743,1630662,6586087,26600572,

%T 107437031,433927396,1752589551,7078534592,28589495207,115470119764,

%U 466372299261,1883631211124,7607798625811,30727139997676,124103854340837

%N Number of n X 3 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

%H R. H. Hardin, <a href="/A231377/b231377.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 16*a(n-3) - 14*a(n-4) - 3*a(n-5) + 8*a(n-6) - 9*a(n-7) - 2*a(n-8) + 6*a(n-9) + 2*a(n-10) for n>11.

%F Empirical g.f.: x*(4 - 3*x + 11*x^2 - 13*x^3 - 6*x^4 - 12*x^5 - 15*x^6 + 3*x^7 + 13*x^8 + 8*x^9 + 2*x^10) / (1 - 6*x + 11*x^2 - 16*x^3 + 14*x^4 + 3*x^5 - 8*x^6 + 9*x^7 + 2*x^8 - 6*x^9 - 2*x^10). - _Colin Barker_, Sep 28 2018

%e Some solutions for n=3:

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

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

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

%Y Column 3 of A231382.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 08 2013

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Last modified September 7 18:28 EDT 2024. Contains 375749 sequences. (Running on oeis4.)