A205221 - OEIS

A205221

Number of (n+1) X 4 0..1 arrays with the number of equal 2 X 2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..1 introduced in row major order.

%I #8 Jun 11 2018 06:32:30

%S 52,132,328,824,2072,5176,13032,32488,81816,203864,513256,1279208,

%T 3218968,8026968,20187368,50370024,126607000,316079576,794071656,

%U 1983434984,4980636824,12446080472,31241340648,78097719912,195970301464

%N Number of (n+1) X 4 0..1 arrays with the number of equal 2 X 2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..1 introduced in row major order.

%C Column 3 of A205226.

%H R. H. Hardin, <a href="/A205221/b205221.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +12*a(n-2) -11*a(n-3) -47*a(n-4) +40*a(n-5) +64*a(n-6) -48*a(n-7) -8*a(n-8) for n>9.

%F Empirical g.f.: 4*x*(13 + 20*x - 107*x^2 - 129*x^3 + 302*x^4 + 237*x^5 - 284*x^6 - 52*x^7 + 16*x^8) / (1 - x - 12*x^2 + 11*x^3 + 47*x^4 - 40*x^5 - 64*x^6 + 48*x^7 + 8*x^8). - _Colin Barker_, Jun 11 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A205226.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 23 2012