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Number of n X 2 0..3 arrays with no element equal the average of immediate neighbors vertically above, diagonally above and left, and horizontally left of it.
1

%I #14 Jul 07 2018 19:29:59

%S 12,130,1430,15724,172936,1901964,20918008,230058424,2530206824,

%T 27827480224,306049553920,3365965156848,37019238613696,

%U 407141477256160,4477784761704800,49247147465796160,541625304181537792

%N Number of n X 2 0..3 arrays with no element equal the average of immediate neighbors vertically above, diagonally above and left, and horizontally left of it.

%C Column 2 of A209019.

%H R. H. Hardin, <a href="/A209013/b209013.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) + 38*a(n-2) - 52*a(n-3) - 40*a(n-4) + 44*a(n-5) - 12*a(n-6).

%F Empirical g.f.: 2*x*(6 + 17*x - 33*x^2 - 16*x^3 + 22*x^4 - 2*x^5) / (1 - 8*x - 38*x^2 + 52*x^3 + 40*x^4 - 44*x^5 + 12*x^6). - _Colin Barker_, Jul 07 2018

%e Some solutions for n=4:

%e 1 0 3 0 1 2 0 1 0 2 1 0 2 3 3 1 0 2 1 3

%e 2 3 0 2 2 3 3 0 2 1 2 3 1 0 1 1 1 2 0 1

%e 3 1 1 0 3 3 1 1 1 0 1 3 0 3 3 3 3 1 1 0

%e 1 0 3 2 2 0 2 0 2 2 3 1 1 0 0 1 0 0 2 0

%Y Cf. A209019.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 04 2012