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A185899 1/8 the number of n X 2 0..7 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors. 1

%I #12 Apr 17 2018 06:16:48

%S 1,15,196,2765,38731,545328,7675381,108065699,1521488668,21421955457,

%T 301612441375,4246586949080,59790307544569,841824567122343,

%U 11852566615920436,166879587240301061,2349600516714827299

%N 1/8 the number of n X 2 0..7 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

%C Column 2 of A185903.

%H R. H. Hardin, <a href="/A185899/b185899.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 13*a(n-1) + 27*a(n-2) - 147*a(n-3) - 245*a(n-4) - 343*a(n-5).

%F Empirical g.f.: x*(1 + 2*x - 26*x^2 - 41*x^3 - 56*x^4) / (1 - 13*x - 27*x^2 + 147*x^3 + 245*x^4 + 343*x^5). - _Colin Barker_, Apr 17 2018

%e Some solutions for 3 X 2 with a(1,1)=0:

%e ..0..1....0..0....0..6....0..0....0..0....0..0....0..0....0..0....0..0....0..7

%e ..0..1....7..0....0..6....0..6....4..0....2..2....5..2....1..1....4..4....0..7

%e ..1..1....7..7....5..5....6..6....4..0....3..3....5..2....3..3....1..1....7..7

%Y Cf. A185903.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 06 2011

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Last modified April 25 08:25 EDT 2024. Contains 371964 sequences. (Running on oeis4.)