A198976 - OEIS

%I #8 Feb 22 2018 16:29:02

%S 1,4,34,481,8731,174454,3603244,75251971,1577395861,33105096904,

%T 695065679254,14595390246661,306496273473391,6436373295247354,

%U 135163500079092064,2838431127851480551,59607037068329713321

%N 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 Column 2 of A198982.

%H R. H. Hardin, <a href="/A198976/b198976.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 32*a(n-1) - 262*a(n-2) + 672*a(n-3) - 441*a(n-4).

%F Conjectures from _Colin Barker_, Feb 22 2018: (Start)

%F G.f.: x*(1 - 28*x + 168*x^2 - 231*x^3) / ((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 21*x)).

%F a(n) = (189 + 56*3^n + 18*7^n + 21^n) / 504.

%F (End)

%e Some solutions with all values from 0 to 5 for n=4:

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

%e ..2..3....2..3....2..3....2..3....2..3....2..3....2..3....2..0....2..0....2..0

%e ..4..5....4..2....1..4....0..4....4..5....4..0....4..5....3..1....3..4....3..4

%e ..2..0....0..5....0..5....2..5....1..2....0..5....0..4....4..5....5..2....0..5

%Y Cf. A198982.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 01 2011