login
Number of n X 2 0..3 arrays x(i,j) with each element horizontally, vertically, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, and upper left element zero.
1

%I #8 Sep 24 2018 12:48:47

%S 0,6,22,200,1732,14384,121696,1027464,8672840,73227432,618256792,

%T 5219942472,44072147576,372102417096,3141672058936,26525234659400,

%U 223953378903736,1890845334033992,15964465905002424,134788481690623048

%N Number of n X 2 0..3 arrays x(i,j) with each element horizontally, vertically, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, and upper left element zero.

%H R. H. Hardin, <a href="/A230964/b230964.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) + 10*a(n-2) + 38*a(n-3) - 132*a(n-4) - 232*a(n-5) - 448*a(n-6) + 320*a(n-7) + 256*a(n-8).

%F Empirical g.f.: 2*x^2*(3 - 10*x - 7*x^2 - 58*x^3 + 108*x^4 + 192*x^5 + 64*x^6) / (1 - 7*x - 10*x^2 - 38*x^3 + 132*x^4 + 232*x^5 + 448*x^6 - 320*x^7 - 256*x^8). - _Colin Barker_, Sep 24 2018

%e Some solutions for n=3:

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

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

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

%Y Column 2 of A230968.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 02 2013