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A204647 Number of (n+1) X 5 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.

%I A204647 #8 Jun 08 2018 10:02:32
%S A204647 48,90,178,330,571,938,1478,2248,3317,4766,6690,9198,12415,16482,
%T A204647 21558,27820,35465,44710,55794,68978,84547,102810,124102,148784,
%U A204647 177245,209902,247202,289622,337671,391890,452854,521172,597489,682486,776882,881434
%N A204647 Number of (n+1) X 5 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 A204647 Column 4 of A204651.
%H A204647 R. H. Hardin, <a href="/A204647/b204647.txt">Table of n, a(n) for n = 1..210</a>
%F A204647 Empirical: a(n) = 5*a(n-1) -9*a(n-2) +5*a(n-3) +5*a(n-4) -9*a(n-5) +5*a(n-6) -a(n-7) for n>9.
%F A204647 Conjectures from _Colin Barker_, Jun 08 2018: (Start)
%F A204647 G.f.: x*(48 - 150*x + 160*x^2 + 10*x^3 - 167*x^4 + 145*x^5 - 43*x^6 - 5*x^7 + 4*x^8) / ((1 - x)^6*(1 + x)).
%F A204647 a(n) = (1920 + 9776*n + 3480*n^2 + 540*n^3 + 90*n^4 + 4*n^5)/480 for n>2 and even.
%F A204647 a(n) = (1950 + 9776*n + 3480*n^2 + 540*n^3 + 90*n^4 + 4*n^5)/480 for n>2 and odd.
%F A204647 (End)
%e A204647 Some solutions for n=5:
%e A204647 ..0..0..0..1..1....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e A204647 ..0..0..0..1..1....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e A204647 ..0..0..1..1..1....0..0..0..0..0....0..0..0..1..1....0..0..0..0..0
%e A204647 ..1..1..1..1..1....0..0..0..0..1....0..0..0..1..1....0..0..0..0..1
%e A204647 ..1..1..1..1..1....0..0..0..0..1....0..1..1..1..1....0..0..0..1..1
%e A204647 ..1..1..1..1..1....0..0..0..1..0....0..1..1..1..1....0..0..1..1..1
%Y A204647 Cf. A204651.
%K A204647 nonn
%O A204647 1,1
%A A204647 _R. H. Hardin_, Jan 17 2012