A230509 - OEIS

A230509

Number of n X 2 0..7 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 8, and upper left element zero.

%I #9 Mar 17 2018 05:46:05

%S 0,0,0,2,8,32,118,440,1664,6354,24360,93440,358246,1372824,5259424,

%T 20147874,77183048,295680992,1132742102,4339515256,16624624832,

%U 63688678130,243990165864,934721535168,3580899428294,13718353772632

%N Number of n X 2 0..7 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 8, and upper left element zero.

%C Column 2 of A230513.

%H R. H. Hardin, <a href="/A230509/b230509.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 4*a(n-2) - 5*a(n-3) + 9*a(n-4) + 12*a(n-5).

%F Empirical g.f.: 2*x^4*(1 - x) / (1 - 5*x + 4*x^2 + 5*x^3 - 9*x^4 - 12*x^5). - _Colin Barker_, Mar 17 2018

%e All solutions for n=4:

%e ..0..7....0..1

%e ..1..6....7..2

%e ..2..5....6..3

%e ..3..4....5..4

%Y Cf. A230513.

%K nonn

%O 1,4

%A _R. H. Hardin_, Oct 21 2013