A207166 - OEIS

%I #8 Jun 19 2018 12:33:24

%S 13,169,624,1612,3445,6513,11284,18304,28197,41665,59488,82524,111709,

%T 148057,192660,246688,311389,388089,478192,583180,704613,844129,

%U 1003444,1184352,1388725,1618513,1875744,2162524,2481037,2833545,3222388,3649984

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

%C Column 5 of A207169.

%H R. H. Hardin, <a href="/A207166/b207166.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (13/4)*n^4 + (13/2)*n^3 + (117/4)*n^2 - 26*n.

%F Conjectures from _Colin Barker_, Jun 19 2018: (Start)

%F G.f.: 13*x*(1 + 8*x - 7*x^2 + 4*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=4:

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

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

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

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

%Y Cf. A207169.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 15 2012