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%I #8 Jun 08 2018 06:41:25
%S 16,32,56,90,137,200,283,390,526,696,906,1162,1471,1840,2277,2790,
%T 3388,4080,4876,5786,6821,7992,9311,10790,12442,14280,16318,18570,
%U 21051,23776,26761,30022,33576,37440,41632,46170,51073,56360,62051,68166,74726,81752
%N Number of (n+1) X 3 0..1 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively.
%C Column 2 of A204651.
%H R. H. Hardin, <a href="/A204645/b204645.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6).
%F Conjectures from _Colin Barker_, Jun 08 2018: (Start)
%F G.f.: x*(16 - 32*x + 8*x^2 + 26*x^3 - 23*x^4 + 6*x^5) / ((1 - x)^5*(1 + x)).
%F a(n) = (576 + 704*n + 232*n^2 + 16*n^3 + 2*n^4)/96 for n even.
%F a(n) = (582 + 704*n + 232*n^2 + 16*n^3 + 2*n^4)/96 for n odd.
%F (End)
%e Some solutions for n=5:
%e ..0..0..0....0..0..1....0..0..0....0..0..0....0..0..0....0..0..1....0..1..1
%e ..0..0..0....0..0..1....0..0..1....0..0..1....0..0..0....0..1..1....0..1..1
%e ..0..0..0....0..0..1....0..1..1....0..0..1....0..0..0....0..1..1....0..1..1
%e ..0..0..0....0..1..1....0..1..1....0..0..1....0..1..1....0..1..1....0..1..1
%e ..0..0..1....0..1..1....0..1..1....0..0..1....1..1..1....1..1..1....0..1..1
%e ..1..1..1....1..1..1....1..1..1....0..0..1....1..1..1....1..1..1....1..1..1
%Y Cf. A204651.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 17 2012
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