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A223777 T(n,k)=Number of nXk 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

%I A223777 #6 Jul 23 2025 04:30:07
%S A223777 2,4,4,7,12,7,11,28,28,11,16,56,78,56,16,22,101,180,180,101,22,29,169,
%T A223777 371,461,371,169,29,37,267,707,1040,1040,707,267,37,46,403,1269,2164,
%U A223777 2516,2164,1269,403,46,56,586,2170,4246,5573,5573,4246,2170,586,56,67
%N A223777 T(n,k)=Number of nXk 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.
%C A223777 Table starts
%C A223777 ..2...4....7....11....16.....22.....29......37......46......56.......67
%C A223777 ..4..12...28....56...101....169....267.....403.....586.....826.....1134
%C A223777 ..7..28...78...180...371....707...1269....2170....3563....5650.....8692
%C A223777 .11..56..180...461..1040...2164...4246....7950...14308...24877....41945
%C A223777 .16.101..371..1040..2516...5573..11635...23230...44703...83305...150815
%C A223777 .22.169..707..2164..5573..12975..28346...59231..119555..234348...447489
%C A223777 .29.267.1269..4246.11635..28346..64256..138913..290180..589799..1170809
%C A223777 .37.403.2170..7950.23230..59231.138913..308895..662370.1382382..2822162
%C A223777 .46.586.3563.14308.44703.119555.290180..662370.1451996.3093428..6448124
%C A223777 .56.826.5650.24877.83305.234348.589799.1382382.3093428.6707709.14215457
%H A223777 R. H. Hardin, <a href="/A223777/b223777.txt">Table of n, a(n) for n = 1..420</a>
%F A223777 Empirical: columns k=1..7 are polynomials of degree 2*k for n> 0,0,0,1,2,3,4
%e A223777 Some solutions for n=3 k=4
%e A223777 ..0..0..1..1....0..0..0..1....0..0..0..0....0..0..0..1....1..0..0..0
%e A223777 ..0..1..1..1....0..0..1..1....0..0..0..0....0..1..1..1....0..0..0..0
%e A223777 ..1..1..1..0....0..1..1..1....0..0..1..0....1..1..1..1....0..0..0..1
%Y A223777 Column 1 is A000124
%Y A223777 Column 2 is A223764
%K A223777 nonn,tabl
%O A223777 1,1
%A A223777 _R. H. Hardin_ Mar 27 2013