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Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock summing to 3 4 or 5.
1

%I #9 Nov 29 2018 10:37:04

%S 51,309,1899,11709,72243,445797,2751003,16976493,104762403,646491861,

%T 3989520459,24619449501,151927356051,937548239301,5785638109947,

%U 35703345104973,220326406088067,1359640814523957,8390383964148267

%N Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock summing to 3 4 or 5.

%H R. H. Hardin, <a href="/A251344/b251344.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) + 3*a(n-2) - 12*a(n-3).

%F Empirical g.f.: 3*x*(17 + x - 36*x^2) / (1 - 6*x - 3*x^2 + 12*x^3). - _Colin Barker_, Nov 29 2018

%e Some solutions for n=4:

%e ..1..1....0..0....1..1....1..0....1..2....2..1....0..2....1..2....2..1....0..0

%e ..1..0....1..2....1..1....1..1....0..1....0..1....1..0....2..0....2..0....2..2

%e ..2..0....2..0....1..2....1..1....1..2....2..0....2..0....1..0....0..2....1..0

%e ..0..1....0..2....0..1....1..1....2..0....2..0....1..2....2..1....2..1....2..0

%e ..2..2....2..0....2..2....2..0....1..0....0..2....0..1....2..0....0..0....2..1

%Y Column 1 of A251351.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 01 2014