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

1,1

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

Links

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

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)

Example

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

Crossrefs

Column 1 is A222993(n+1)

Sequence in context: A097371 A179755 A186843 * A251065 A231087 A235956

Adjacent sequences: A250524 A250525 A250526 * A250528 A250529 A250530

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 24 2014

Status

approved