|
%I #8 Jan 17 2016 17:53:39
%S 2,3,3,4,7,4,5,13,15,5,6,22,42,31,6,7,34,105,141,63,7,8,50,232,567,
%T 486,127,8,9,70,475,1986,3351,1685,255,9,10,95,904,6292,20040,20676,
%U 5804,511,10,11,125,1632,18205,107015,220235,129129,19769,1023,11,12,161,2806
%N T(n,k)=Number of nXk binary arrays with row sums nondecreasing and columns lexicographically nondecreasing.
%C Table starts
%C ..2....3......4........5..........6............7..............8
%C ..3....7.....13.......22.........34...........50.............70
%C ..4...15.....42......105........232..........475............904
%C ..5...31....141......567.......1986.........6292..........18205
%C ..6...63....486.....3351......20040.......107015.........516084
%C ..7..127...1685....20676.....220235......2093467.......17892539
%C ..8..255...5804...129129....2499080.....43555569......683027146
%C ..9..511..19769...804817...28501471....924051709....27044976947
%C .10.1023..66544..4982759..323067002..19614050515..1079112886476
%C .11.2047.221581.30629206.3626695952.413556580944.42860145907558
%H R. H. Hardin, <a href="/A267245/b267245.txt">Table of n, a(n) for n = 1..216</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)
%F k=3: a(n) = 10*a(n-1) -39*a(n-2) +76*a(n-3) -79*a(n-4) +42*a(n-5) -9*a(n-6)
%F k=4: [order 10]
%F k=5: [order 14]
%F k=6: [order 22]
%F k=7: [order 32]
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1) -a(n-2)
%F n=2: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5)
%F n=3: [order 13]
%e Some solutions for n=4 k=4
%e ..0..0..1..1....0..0..0..1....0..0..1..1....0..0..1..1....0..0..1..1
%e ..0..1..1..1....0..1..1..0....0..1..0..1....1..1..0..0....1..1..0..0
%e ..1..0..1..1....0..0..1..1....1..1..0..0....1..1..0..1....1..1..0..0
%e ..1..1..0..1....1..0..1..0....1..1..0..0....1..1..1..0....1..1..0..0
%Y Column 1 and row 1 are A000027(n+1).
%Y Column 2 is A000225(n+1).
%Y Row 2 is A002623.
%Y Row 3 is A233302(n-1).
%Y Row 4 is A233303(n-1).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 12 2016
| 