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Number of nX5 binary arrays with rows and columns in nondecreasing order
1

%I #5 Mar 31 2012 12:35:56

%S 6,41,336,2942,24520,183010,1202234,6979061,36211867,170079565,

%T 731624096,2911895183,10815978253,37768115174,124748330554,

%U 391810133592,1175449312215,3381493985527,9359644588182,25000202714062,64609485660764

%N Number of nX5 binary arrays with rows and columns in nondecreasing order

%C Column 5 of A180985

%H R. H. Hardin, <a href="/A184140/b184140.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n)=32*a(n-1)-496*a(n-2)+4960*a(n-3)-35960*a(n-4)+201376*a(n-5)-906192*a(n-6)+3365856*a(n-7)-10518300*a(n-8)+28048800*a(n-9)-64512240*a(n-10)+129024480*a(n-11)-225792840*a(n-12)+347373600*a(n-13)-471435600*a(n-14)+565722720*a(n-15)-601080390*a(n-16)+565722720*a(n-17)-471435600*a(n-18)+347373600*a(n-19)-225792840*a(n-20)+129024480*a(n-21)-64512240*a(n-22)+28048800*a(n-23)-10518300*a(n-24)+3365856*a(n-25)-906192*a(n-26)+201376*a(n-27)-35960*a(n-28)+4960*a(n-29)-496*a(n-30)+32*a(n-31)-a(n-32) (=polynomial degree 31)

%e Some solutions for 3X5

%e ..0..0..1..1..1....0..1..1..1..1....0..0..1..1..1....0..0..0..0..1

%e ..0..1..0..1..1....1..0..0..0..0....0..1..0..0..0....0..1..1..1..1

%e ..1..1..0..0..1....1..1..1..1..1....1..1..1..1..1....1..0..0..0..0

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 09 2011