A266428 - OEIS

%I #6 Dec 29 2015 10:13:21

%S 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 50,8,9,92,574,1556,1391,433,70,9,10,129,1170,5365,8764,4383,826,95,

%U 10,11,175,2223,16585,49894,45907,12758,1493,125,11,12,231,3982,46463,251381

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

%C Table starts

%C ..2...3....4......5........6..........7............8............9

%C ..3...7...14.....25.......41.........63...........92..........129

%C ..4..13...39....106......259........574.........1170.........2223

%C ..5..22...96....404.....1556.......5365........16585........46463

%C ..6..34..212...1391.....8764......49894.......251381......1122721

%C ..7..50..433...4383....45907.....448649......3889553.....29520031

%C ..8..70..826..12758...223075....3825307.....59155748....798834778

%C ..9..95.1493..34611..1005991...30555624....861030491..21325003746

%C .10.125.2575..88206..4224203..227542455..11809616668.546283341439

%C .11.161.4270.212609.16588684.1579153474.151566391972

%H R. H. Hardin, <a href="/A266428/b266428.txt">Table of n, a(n) for n = 1..145</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) -a(n-2)

%F k=2: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5)

%F k=3: [order 12] Empirical for row n:

%F n=1: a(n) = n + 1

%F n=2: a(n) = (1/6)*n^3 + (1/2)*n^2 + (4/3)*n + 1

%F n=3: [polynomial of degree 6]

%F n=4: [polynomial of degree 11]

%F n=5: [polynomial of degree 19]

%F n=6: [polynomial of degree 33]

%F n=7: [polynomial of degree 57]

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 and row 1 are A000027(n+1).

%Y Column 2 is A002623.

%Y Row 2 is A004006(n+1).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 29 2015