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%I #7 Jan 09 2019 09:12:34
%S 1,2,6,2,3,9,9,16,27,35,55,105,145,202,369,589,857,1371,2229,3444,
%T 5411,8585,13399,21170,33573,52488,82413,130606,205585,322481,508515,
%U 801862,1261277,1985864,3128187,4924251,7755005,12214150,19226531,30273410
%N Number of 3 X n integer arrays with each element equal to the number of horizontal and antidiagonal neighbors not equal to itself.
%H R. H. Hardin, <a href="/A265993/b265993.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 2*a(n-3) + a(n-4) - 3*a(n-5) - a(n-6) - a(n-7) + a(n-8) + 7*a(n-9) - 2*a(n-10) - 4*a(n-11) + 9*a(n-14) + 3*a(n-15) - 8*a(n-16) - 4*a(n-17) for n>20.
%F Empirical g.f.: x*(1 + x + 4*x^2 - 6*x^3 - 4*x^4 - 5*x^5 - 3*x^6 + 20*x^7 + 3*x^8 - 11*x^9 - 7*x^10 - 17*x^11 + 12*x^12 + 16*x^13 - 17*x^14 - 18*x^15 - 13*x^16 - 3*x^17 + 8*x^18 + 4*x^19) / ((1 - x)*(1 + x^2 - x^3 - x^4 + 3*x^7 + 2*x^8)*(1 - x^2 - x^3 - x^4 - 3*x^7 - 2*x^8)). - _Colin Barker_, Jan 09 2019
%e Some solutions for n=6:
%e ..1..3..1..1..3..2....1..3..2..2..3..1....1..3..1..1..1..2....1..3..1..1..3..2
%e ..1..1..1..1..1..1....2..3..3..4..1..1....1..1..4..1..1..1....2..1..1..1..1..1
%e ..2..3..1..1..3..1....1..1..1..1..3..1....1..3..1..1..3..1....1..3..1..1..3..1
%Y Row 3 of A265991.
%K nonn
%O 1,2
%A _R. H. Hardin_, Dec 19 2015
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