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A226866 Number of n X 2 (-1,0,1) arrays of determinants of 2 X 2 subblocks of some (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order. 1

%I

%S 4,13,37,91,199,397,736,1285,2134,3397,5215,7759,11233,15877,21970,

%T 29833,39832,52381,67945,87043,110251,138205,171604,211213,257866,

%U 312469,376003,449527,534181,631189,741862,867601,1009900,1170349,1350637

%N Number of n X 2 (-1,0,1) arrays of determinants of 2 X 2 subblocks of some (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.

%H R. H. Hardin, <a href="/A226866/b226866.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/40)*n^5 + (7/8)*n^3 + (21/10)*n + 1.

%F Conjectures from _Colin Barker_, Sep 06 2018: (Start)

%F G.f.: x*(4 - 11*x + 19*x^2 - 16*x^3 + 8*x^4 - x^5) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A226870.

%K nonn

%O 1,1

%A _R. H. Hardin_ Jun 20 2013

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Last modified May 19 17:48 EDT 2019. Contains 323395 sequences. (Running on oeis4.)