A208284 - OEIS

%I #8 Jun 29 2018 11:37:46

%S 16,256,1260,3984,9900,21096,40376,71360,118584,187600,285076,418896,

%T 598260,833784,1137600,1523456,2006816,2604960,3337084,4224400,

%U 5290236,6560136,8061960,9825984,11885000,14274416,17032356,20199760,23820484

%N Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

%C Column 5 of A208287.

%H R. H. Hardin, <a href="/A208284/b208284.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (5/6)*n^5 + 9*n^4 + (91/6)*n^3 - 9*n^2.

%F Conjectures from _Colin Barker_, Jun 29 2018: (Start)

%F G.f.: 4*x*(2 - x)*(2 + 21*x + 6*x^2 - 4*x^3) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A208287.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 25 2012