A231242 - OEIS

%I #7 Sep 27 2018 15:34:15

%S 0,44,464,5992,76136,968824,12322784,156753000,1993963288,25364073040,

%T 322641895760,4104143547136,52206469041840,664088714466040,

%U 8447493744195456,107455749517836112,1366883297468138664

%N Number of n X 4 0..3 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.

%H R. H. Hardin, <a href="/A231242/b231242.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) + 30*a(n-2) + 53*a(n-3) + 71*a(n-4) - a(n-5) + 6*a(n-6) - 8*a(n-7).

%F Empirical g.f.: 4*x^2*(11 + 6*x + 8*x^2 - 9*x^3 - 3*x^4 - 3*x^5) / (1 - 10*x - 30*x^2 - 53*x^3 - 71*x^4 + x^5 - 6*x^6 + 8*x^7). - _Colin Barker_, Sep 27 2018

%e Some solutions for n=4:

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

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

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

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

%Y Column 4 of A231246.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 06 2013