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A188416 T(n,k)=Number of (n*k)Xk binary arrays with rows in nonincreasing order, n ones in every column and no more than 3 ones in any row.

%I A188416 #7 Jul 22 2025 11:11:59
%S A188416 1,2,1,5,3,1,14,16,4,1,46,124,39,5,1,166,1308,723,81,6,1,652,17443,
%T A188416 21965,3217,150,7,1,2780,282349,968230,252493,11712,256,8,1,12644,
%U A188416 5396178,57967660,33313408,2181522,36659,410,9,1,61136,119324602,4505774905
%N A188416 T(n,k)=Number of (n*k)Xk binary arrays with rows in nonincreasing order, n ones in every column and no more than 3 ones in any row.
%C A188416 Table starts
%C A188416 .1..2....5.....14........46..........166............652............2780
%C A188416 .1..3...16....124......1308........17443.........282349.........5396178
%C A188416 .1..4...39....723.....21965.......968230.......57967660......4505774905
%C A188416 .1..5...81...3217....252493.....33313408.....6720357785...1943505834628
%C A188416 .1..6..150..11712...2181522....793369090...498407294632.497114063711190
%C A188416 .1..7..256..36659..15083334..14100262412.25784105550034
%C A188416 .1..8..410.101829..87171345.197263686098
%C A188416 .1..9..625.256901.434626896
%C A188416 .1.10..915.598561
%C A188416 .1.11.1296
%H A188416 R. H. Hardin, <a href="/A188416/b188416.txt">Table of n, a(n) for n = 1..80</a>
%e A188416 All solutions for 6X2
%e A188416 ..1..1....1..1....1..0....1..1
%e A188416 ..1..0....1..1....1..0....1..1
%e A188416 ..1..0....1..1....1..0....1..0
%e A188416 ..0..1....0..0....0..1....0..1
%e A188416 ..0..1....0..0....0..1....0..0
%e A188416 ..0..0....0..0....0..1....0..0
%Y A188416 Column 3 is A011863(n+1)
%Y A188416 Row 1 is A001680
%K A188416 nonn,tabl
%O A188416 1,2
%A A188416 _R. H. Hardin_ Mar 30 2011