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Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
1

%I #10 Jun 18 2018 12:29:08

%S 9,81,288,720,1485,2709,4536,7128,10665,15345,21384,29016,38493,50085,

%T 64080,80784,100521,123633,150480,181440,216909,257301,303048,354600,

%U 412425,477009,548856,628488,716445,813285,919584,1035936,1162953

%N Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.

%C Column 4 of A207068.

%H R. H. Hardin, <a href="/A207064/b207064.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (3/4)*n^4 + (15/2)*n^3 + (15/4)*n^2 - 3*n.

%F Conjectures from _Colin Barker_, Jun 18 2018: (Start)

%F G.f.: 9*x*(1 + 4*x - 3*x^2) / (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..0..0..0....0..0..0..0....1..1..1..1....1..1..0..0....0..0..0..0

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

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

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

%Y Cf. A207068.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 14 2012