A207452 - OEIS

%I #11 Jun 23 2018 05:49:28

%S 42,1764,10710,36456,92610,196812,370734,640080,1034586,1588020,

%T 2338182,3326904,4600050,6207516,8203230,10645152,13595274,17119620,

%U 21288246,26175240,31858722,38420844,45947790,54529776,64261050,75239892,87568614

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

%C Column 7 of A207453.

%H R. H. Hardin, <a href="/A207452/b207452.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 168*n^4 - 84*n^3 - 84*n^2 + 42*n.

%F Conjectures from _Colin Barker_, Jun 23 2018: (Start)

%F G.f.: 42*x*(1 + 37*x + 55*x^2 + 3*x^3) / (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=5:

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

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

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

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

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

%Y Cf. A207453.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 17 2012