A208140 - OEIS

%I #8 Jun 28 2018 14:35:49

%S 16,256,1600,6400,19600,50176,112896,230400,435600,774400,1308736,

%T 2119936,3312400,5017600,7398400,10653696,15023376,20793600,28302400,

%U 37945600,50183056,65545216,84640000,108160000,136890000,171714816

%N Number of n X 6 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

%C Column 6 of A208142.

%H R. H. Hardin, <a href="/A208140/b208140.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (4/9)*n^6 + (8/3)*n^5 + (52/9)*n^4 + (16/3)*n^3 + (16/9)*n^2.

%F Conjectures from _Colin Barker_, Jun 28 2018: (Start)

%F G.f.: 16*x*(1 + x)*(1 + 8*x + x^2) / (1 - x)^7.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

%F (End)

%e Some solutions for n=4:

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

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

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

%Y Cf. A208142.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 23 2012