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Number of n X 5 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors equal to itself.
1

%I #7 Jan 09 2019 09:12:54

%S 1,4,11,27,70,182,483,1281,3389,8986,23818,63151,167404,443816,

%T 1176578,3119246,8269369,21922921,58119638,154080691,408482159,

%U 1082924551,2870933873,7611114236,20177774274,53493165081,141815376408,375965811006

%N Number of n X 5 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors equal to itself.

%H R. H. Hardin, <a href="/A266009/b266009.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3) + 2*a(n-4) - 3*a(n-5) - a(n-6) for n>12.

%F Empirical g.f.: x*(1 + 2*x + x^2 - 2*x^3 - 4*x^4 - 6*x^5 - 3*x^6 + 4*x^7 - 5*x^8 + 2*x^9 - x^10 + x^11) / ((1 - x)*(1 + x^2)*(1 - x - 4*x^2 - x^3)). - _Colin Barker_, Jan 09 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 5 of A266012.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 20 2015