A230529 - OEIS

A230529

Number of n X 2 0..6 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 7, and upper left element zero.

%I #16 Jun 07 2018 19:34:46

%S 0,0,0,0,0,0,2,8,32,120,432,1512,5182,17500,58432,193360,635296,

%T 2075248,6746882,21848960,70523816,227010760,729035536,2336660440,

%U 7476771198,23889669636,76238228904,243039699792,774082314048,2463524146272

%N Number of n X 2 0..6 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 7, and upper left element zero.

%C Column 2 of A230533.

%H R. H. Hardin, <a href="/A230529/b230529.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 4*a(n-3) - 8*a(n-4) - 12*a(n-5) - 17*a(n-6) - 10*a(n-7).

%F Empirical g.f.: 2*x^7 / (1 - 4*x + 4*x^3 + 8*x^4 + 12*x^5 + 17*x^6 + 10*x^7). - _Colin Barker_, Mar 17 2018

%e All solutions for n=7:

%e ..0..6....0..1

%e ..1..5....6..2

%e ..2..4....5..3

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

%e ..4..2....3..5

%e ..5..1....2..6

%e ..6..0....1..0

%Y Cf. A230533.

%K nonn

%O 1,7

%A _R. H. Hardin_, Oct 22 2013