A188823 - OEIS

%I #10 Apr 30 2018 13:56:18

%S 256,3025,11664,28561,53824,87616,129600,179776,238144,304704,379456,

%T 462400,553536,652864,760384,876096,1000000,1132096,1272384,1420864,

%U 1577536,1742400,1915456,2096704,2286144,2483776,2689600,2903616,3125824

%N Number of n X 8 binary arrays without the pattern 0 1 diagonally or antidiagonally.

%C Column 8 of A188824.

%H R. H. Hardin, <a href="/A188823/b188823.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 4096*n^2 - 11264*n + 7744 for n>4.

%F Empirical g.f.: x*(256 + 2257*x + 3357*x^2 + 2388*x^3 + 108*x^4 + 163*x^5 - 337*x^6) / (1 - x)^3. - _Colin Barker_, Apr 30 2018

%e Some solutions for 3 X 8:

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

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

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

%Y Cf. A188824.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 11 2011