A250527 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction.

50, 222, 222, 867, 1180, 867, 3123, 5029, 5029, 3123, 10660, 18859, 21955, 18859, 10660, 35064, 65310, 82023, 82023, 65310, 35064, 112373, 214812, 279161, 300131, 279161, 214812, 112373, 353517, 682921, 896191, 993123, 993123, 896191, 682921

Offset: 1

Author

R. H. Hardin, Nov 24 2014

Keywords

• nonn
• tabl

Comments

Table starts

......50......222......867......3123.....10660......35064.....112373.....353517

.....222.....1180.....5029.....18859.....65310.....214812.....682921....2122743

.....867.....5029....21955.....82023....279161.....896191....2771901....8374485

....3123....18859....82023....300131....993123....3088923....9240559...26984403

...10660....65310...279161....993123...3183434....9580060...27710543...78195145

...35064...214812...896191...3088923...9580060...27910024...78204775..213775147

..112373...682921..2771901...9240559..27710543...78204775..212707851..565044857

..353517..2122743..8374485..26984403..78195145..213775147..565044857.1462376991

.1097430..6501118.24944039..77707851.217483704..575554760.1478308633.3731976469

.3374226.19720580.73714737.222271083.600720730.1537251580.3832617341.9435234815

Examples

			Some solutions for n=3 k=4
..2..2..1..1..0....2..2..1..1..0....2..1..0..0..1....2..2..1..0..0
..2..2..1..1..0....1..1..0..1..0....1..0..0..0..1....1..1..1..0..0
..1..1..1..1..1....0..2..1..2..1....2..1..1..1..2....1..1..2..1..1
..1..2..2..2..2....0..2..1..2..2....1..0..0..0..1....1..1..2..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..241

Crossrefs

Column 1 is A222993(n+1)

Formula

Empirical for column k (k=2 recurrence also works for k=1):

k=1: a(n) = 9*a(n-1) -31*a(n-2) +51*a(n-3) -40*a(n-4) +12*a(n-5)

k=2-7: a(n) = 14*a(n-1) -85*a(n-2) +294*a(n-3) -639*a(n-4) +906*a(n-5) -839*a(n-6) +490*a(n-7) -164*a(n-8) +24*a(n-9)