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A266428 T(n,k)=Number of nXk binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

%I A266428 #6 Dec 29 2015 10:13:21
%S A266428 2,3,3,4,7,4,5,14,13,5,6,25,39,22,6,7,41,106,96,34,7,8,63,259,404,212,
%T A266428 50,8,9,92,574,1556,1391,433,70,9,10,129,1170,5365,8764,4383,826,95,
%U A266428 10,11,175,2223,16585,49894,45907,12758,1493,125,11,12,231,3982,46463,251381
%N A266428 T(n,k)=Number of nXk binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.
%C A266428 Table starts
%C A266428 ..2...3....4......5........6..........7............8............9
%C A266428 ..3...7...14.....25.......41.........63...........92..........129
%C A266428 ..4..13...39....106......259........574.........1170.........2223
%C A266428 ..5..22...96....404.....1556.......5365........16585........46463
%C A266428 ..6..34..212...1391.....8764......49894.......251381......1122721
%C A266428 ..7..50..433...4383....45907.....448649......3889553.....29520031
%C A266428 ..8..70..826..12758...223075....3825307.....59155748....798834778
%C A266428 ..9..95.1493..34611..1005991...30555624....861030491..21325003746
%C A266428 .10.125.2575..88206..4224203..227542455..11809616668.546283341439
%C A266428 .11.161.4270.212609.16588684.1579153474.151566391972
%H A266428 R. H. Hardin, <a href="/A266428/b266428.txt">Table of n, a(n) for n = 1..145</a>
%F A266428 Empirical for column k:
%F A266428 k=1: a(n) = 2*a(n-1) -a(n-2)
%F A266428 k=2: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5)
%F A266428 k=3: [order 12] Empirical for row n:
%F A266428 n=1: a(n) = n + 1
%F A266428 n=2: a(n) = (1/6)*n^3 + (1/2)*n^2 + (4/3)*n + 1
%F A266428 n=3: [polynomial of degree 6]
%F A266428 n=4: [polynomial of degree 11]
%F A266428 n=5: [polynomial of degree 19]
%F A266428 n=6: [polynomial of degree 33]
%F A266428 n=7: [polynomial of degree 57]
%e A266428 Some solutions for n=4 k=4
%e A266428 ..0..0..0..0....0..0..1..1....0..0..0..1....0..0..1..1....0..0..0..1
%e A266428 ..0..0..0..1....0..0..1..1....0..0..1..0....0..1..0..1....0..1..1..1
%e A266428 ..0..0..1..1....1..1..0..1....0..1..1..1....0..1..1..1....0..1..1..1
%e A266428 ..0..1..0..1....1..1..1..0....1..1..0..0....1..1..1..0....1..0..0..1
%Y A266428 Column 1 and row 1 are A000027(n+1).
%Y A266428 Column 2 is A002623.
%Y A266428 Row 2 is A004006(n+1).
%K A266428 nonn,tabl
%O A266428 1,1
%A A266428 _R. H. Hardin_, Dec 29 2015