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A204649 Number of (n+1) X 7 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 A204649 #8 Jun 08 2018 13:51:25
%S A204649 132,200,434,938,1918,3702,6780,11868,19969,32450,51134,78404,117324,
%T A204649 171774,246604,347804,482695,660138,890766,1187236,1564506,2040134,
%U A204649 2634604,3371676,4278765,5387346,6733390,8357828,10307048,12633422
%N A204649 Number of (n+1) X 7 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 A204649 Column 6 of A204651.
%H A204649 R. H. Hardin, <a href="/A204649/b204649.txt">Table of n, a(n) for n = 1..210</a>
%F A204649 Empirical: a(n) = 7*a(n-1) -20*a(n-2) +28*a(n-3) -14*a(n-4) -14*a(n-5) +28*a(n-6) -20*a(n-7) +7*a(n-8) -a(n-9) for n>13.
%F A204649 Empirical g.f.: x*(132 - 724*x + 1674*x^2 - 1796*x^3 + 280*x^4 + 1532*x^5 - 1858*x^6 + 992*x^7 - 255*x^8 + 15*x^9 + 26*x^10 - 22*x^11 + 6*x^12) / ((1 - x)^8*(1 + x)). - _Colin Barker_, Jun 08 2018
%e A204649 Some solutions for n=5:
%e A204649 ..0..0..0..1..1..1..1....0..0..0..0..0..0..1....0..0..0..0..0..0..0
%e A204649 ..0..0..1..1..1..1..1....0..0..0..0..0..0..1....0..0..0..0..0..1..1
%e A204649 ..0..0..1..1..1..1..1....0..0..0..0..0..0..1....0..0..1..1..1..1..1
%e A204649 ..0..0..1..1..1..1..1....0..0..0..0..1..1..1....0..0..1..1..1..1..1
%e A204649 ..0..0..1..1..1..1..1....0..0..0..1..1..1..1....0..1..1..1..1..1..1
%e A204649 ..0..1..1..1..1..1..1....1..1..1..1..1..1..1....1..1..1..1..1..1..1
%Y A204649 Cf. A204651.
%K A204649 nonn
%O A204649 1,1
%A A204649 _R. H. Hardin_, Jan 17 2012