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A204643 Number of (n+1)X(n+1) 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 A204643 #8 Jul 22 2025 18:12:13
%S A204643 8,32,104,330,1076,3702,13314,49312,185786,706912,2706218,10403402,
%T A204643 40120324,155122378,601086622,2333614100,9075145134,35345275932,
%U A204643 137846543630,538257892350,2104098985192,8233430753142,32247603713264
%N A204643 Number of (n+1)X(n+1) 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 A204643 Diagonal of A204651
%H A204643 R. H. Hardin, <a href="/A204643/b204643.txt">Table of n, a(n) for n = 1..63</a>
%e A204643 Some solutions for n=5
%e A204643 ..0..0..0..0..0..1....0..0..0..0..1..1....0..0..0..0..0..1....0..0..0..0..0..0
%e A204643 ..0..0..1..1..1..1....0..0..0..0..1..1....0..0..0..0..1..1....0..0..0..0..0..0
%e A204643 ..0..0..1..1..1..1....0..0..0..1..1..1....0..0..0..0..1..1....0..0..0..0..1..1
%e A204643 ..0..1..1..1..1..1....0..0..1..1..1..1....0..0..0..0..1..1....0..0..0..0..1..1
%e A204643 ..1..1..1..1..1..1....0..1..1..1..1..1....0..0..0..1..1..1....0..1..1..1..1..1
%e A204643 ..1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1
%K A204643 nonn
%O A204643 1,1
%A A204643 _R. H. Hardin_ Jan 17 2012