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A198976 Number of n X 2 0..5 arrays with values 0..5 introduced in row major order and no element equal to any horizontal or vertical neighbor.

%I A198976 #8 Feb 22 2018 16:29:02
%S A198976 1,4,34,481,8731,174454,3603244,75251971,1577395861,33105096904,
%T A198976 695065679254,14595390246661,306496273473391,6436373295247354,
%U A198976 135163500079092064,2838431127851480551,59607037068329713321
%N A198976 Number of n X 2 0..5 arrays with values 0..5 introduced in row major order and no element equal to any horizontal or vertical neighbor.
%C A198976 Column 2 of A198982.
%H A198976 R. H. Hardin, <a href="/A198976/b198976.txt">Table of n, a(n) for n = 1..200</a>
%F A198976 Empirical: a(n) = 32*a(n-1) - 262*a(n-2) + 672*a(n-3) - 441*a(n-4).
%F A198976 Conjectures from _Colin Barker_, Feb 22 2018: (Start)
%F A198976 G.f.: x*(1 - 28*x + 168*x^2 - 231*x^3) / ((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 21*x)).
%F A198976 a(n) = (189 + 56*3^n + 18*7^n + 21^n) / 504.
%F A198976 (End)
%e A198976 Some solutions with all values from 0 to 5 for n=4:
%e A198976 ..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
%e A198976 ..2..3....2..3....2..3....2..3....2..3....2..3....2..3....2..0....2..0....2..0
%e A198976 ..4..5....4..2....1..4....0..4....4..5....4..0....4..5....3..1....3..4....3..4
%e A198976 ..2..0....0..5....0..5....2..5....1..2....0..5....0..4....4..5....5..2....0..5
%Y A198976 Cf. A198982.
%K A198976 nonn
%O A198976 1,2
%A A198976 _R. H. Hardin_, Nov 01 2011