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%I #24 Dec 23 2016 22:55:03
%S 3,3,7,7,14,14,25,25,41,41,63,63,92,92,129,129,175,175,231,231,298,
%T 298,377,377,469,469,575,575,696,696,833,833,987,987,1159,1159,1350,
%U 1350,1561,1561,1793,1793,2047,2047,2324,2324,2625,2625,2951,2951,3303,3303
%N Number of (n+1) X (3+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits, and rows and columns lexicographically nonincreasing.
%C Column 3 of A263799.
%H R. H. Hardin, <a href="/A263794/b263794.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7).
%F Empirical: a(n) = A058187(n-1) + floor((n+3)/2). - _Filip Zaludek_, Dec 14 2016
%F Conjectures from _Colin Barker_, Dec 14 2016: (Start)
%F a(n) = (n^3 + 6*n^2 + 32*n + 48)/48 for n even.
%F a(n) = (n^3 + 9*n^2 + 47*n + 87)/48 for n odd.
%F G.f.: x*(3 - 5*x^2 + 4*x^4 - x^6) / ((1 - x)^4*(1 + x)^3).
%F (End)
%e Some solutions for n = 5:
%e 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 0 0
%e 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 0 0
%e 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0
%e 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0
%e 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0
%e 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0
%Y Cf. A058187, A263799.
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 26 2015
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