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A204650 Number of (n+1) X 8 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 A204650 #11 Jun 09 2018 18:57:48
%S A204650 216,283,637,1478,3261,6780,13314,24862,44426,76378,126906,204583,
%T A204650 321038,491781,737163,1083525,1564519,2222657,3111073,4295556,5856841,
%U A204650 7893218,10523448,13890048,18162936,23543500,30269084,38617957,48914760,61536499
%N A204650 Number of (n+1) X 8 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 A204650 Column 7 of A204651.
%H A204650 R. H. Hardin, <a href="/A204650/b204650.txt">Table of n, a(n) for n = 1..210</a>
%F A204650 Empirical: a(n) = 8*a(n-1) - 27*a(n-2) + 48*a(n-3) - 42*a(n-4) + 42*a(n-6) - 48*a(n-7) + 27*a(n-8) - 8*a(n-9) + a(n-10) for n > 15.
%F A204650 Empirical g.f.: x*(216 - 1445*x + 4205*x^2 - 6345*x^3 + 4124*x^4 + 1908*x^5 - 6141*x^6 + 5440*x^7 - 2472*x^8 + 519*x^9 + 27*x^10 - 28*x^11 - 24*x^12 + 24*x^13 - 6*x^14) / ((1 - x)^9*(1 + x)). - _Colin Barker_, Jun 08 2018
%e A204650 Some solutions for n=5:
%e A204650   1 0 1 0 1 0 0 1       0 0 0 0 0 0 0 0       0 0 0 0 0 0 0 1
%e A204650   0 1 0 1 0 1 1 1       0 0 0 0 0 0 0 1       0 0 0 0 0 0 0 1
%e A204650   1 0 1 0 1 1 1 1       0 0 0 0 0 0 0 1       0 0 0 0 0 0 1 1
%e A204650   0 1 0 1 1 1 1 1       0 0 0 1 1 1 1 1       0 0 0 0 0 1 1 1
%e A204650   1 0 1 1 1 1 1 1       1 1 1 1 1 1 1 1       0 0 0 0 0 1 1 1
%e A204650   0 1 1 1 1 1 1 1       1 1 1 1 1 1 1 1       1 1 1 1 1 1 1 1
%Y A204650 Cf. A204651.
%K A204650 nonn
%O A204650 1,1
%A A204650 _R. H. Hardin_, Jan 17 2012