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A263794 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.

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