A207168 - OEIS

%I #8 Jun 20 2018 09:46:01

%S 28,784,3808,11452,26908,54208,98224,164668,260092,391888,568288,

%T 798364,1092028,1460032,1913968,2466268,3130204,3919888,4850272,

%U 5937148,7197148,8647744,10307248,12194812,14330428,16734928,19429984,22438108,25782652

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

%C Column 7 of A207169.

%H R. H. Hardin, <a href="/A207168/b207168.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 35*n^4 + 42*n^3 + 7*n^2 - 84*n + 28.

%F Conjectures from _Colin Barker_, Jun 20 2018: (Start)

%F G.f.: 28*x*(1 + 23*x + 6*x^2 - x^3 + x^4) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A207169.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 15 2012