A188839 - OEIS

%I #8 Apr 30 2018 13:54:29

%S 32,144,364,728,1288,2108,3264,4845,6954,9709,13244,17710,23276,30130,

%T 38480,48555,60606,74907,91756,111476,134416,160952,191488,226457,

%U 266322,311577,362748,420394,485108,557518,638288,728119,827750,937959,1059564

%N Number of n X 5 binary arrays without the pattern 0 1 diagonally or vertically.

%C Column 5 of A188843.

%H R. H. Hardin, <a href="/A188839/b188839.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (1/120)*n^5 + (7/24)*n^4 + (89/24)*n^3 + (473/24)*n^2 + (1877/60)*n - 33 for n>2.

%F Empirical g.f.: x*(32 - 48*x - 20*x^2 + 64*x^3 - 20*x^4 - 12*x^5 + 4*x^6 + x^7) / (1 - x)^6. - _Colin Barker_, Apr 30 2018

%e Some solutions for 3 X 5:

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

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

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

%Y Cf. A188843.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 12 2011