A208141 - OEIS

%I #8 Jun 28 2018 14:35:57

%S 20,400,3000,14000,49000,141120,352800,792000,1633500,3146000,5725720,

%T 9937200,16562000,26656000,41616000,63256320,93896100,136458000,

%U 194579000,272734000,376372920,512072000,687700000,912600000,1197787500

%N Number of n X 7 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

%C Column 7 of A208142.

%H R. H. Hardin, <a href="/A208141/b208141.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (5/36)*n^7 + (5/4)*n^6 + (155/36)*n^5 + (85/12)*n^4 + (50/9)*n^3 + (5/3)*n^2.

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

%F G.f.: 20*x*(1 + 12*x + 18*x^2 + 4*x^3) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

%F (End)

%e Some solutions for n=4:

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

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

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

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