A250632 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 min(x(i,j),x(i-1,j)) in the j direction

36, 154, 125, 585, 654, 380, 2183, 2969, 2347, 1072, 7924, 12360, 12151, 7342, 2856, 28456, 49310, 56232, 43185, 20743, 7307, 101308, 190213, 241742, 218680, 134878, 53847, 18131, 358990, 720347, 994030, 1014946, 747039, 381834, 130848, 43966

Offset

1,1

Comments

Table starts

.....36.....154......585.....2183......7924......28456......101308.......358990

....125.....654.....2969....12360.....49310.....190213......720347......2690076

....380....2347....12151....56232....241742.....994030.....3951204.....15376595

...1072....7342....43185...218680...1014946....4416061....18465586.....74732823

...2856...20743...134878...747039...3719562...17202711....75537881....319253573

...7307...53847...381834..2290189..12291286...60472234...280151655...1237636447

..18131..130848...994281..6421141..37072806..195029867...955747123...4434468137

..43966..300960..2419996.16675794.103697021..584383121..3044656152..14889326715

.104755..662000..5560799.40596068.271291108.1641320797..9115002626..47182771424

.246252.1402495.12176364.93379730.669808747.4350649060.25819633391.141867614165

Links

R. H. Hardin, Table of n, a(n) for n = 1..480

Formula

Empirical for column k:

k=1: [linear recurrence of order 9]

k=2: [order 14]

k=3: [order 20]

k=4: [order 21] for n>24; also a degree 14 polynomial plus a degree 5 quasipolynomial with period 2

k=5: [order 22] for n>29; also a degree 14 polynomial plus a degree 6 quasipolynomial with period 2

k=6: [order 25] for n>36; also a degree 16 polynomial plus a degree 7 quasipolynomial with period 2

k=7: [order 28] for n>43; also a degree 18 polynomial plus a degree 8 quasipolynomial with period 2

Empirical for row n:

n=1: [linear recurrence of order 8]

n=2: [order 13] for n>16

n=3: [order 26] for n>29

n=4: [order 33] for n>37

n=5: [order 49] for n>54

n=6: [order 57] for n>63

n=7: [order 79] for n>86

Example

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

Crossrefs

Sequence in context: A160754 A275496 A117511 * A211728 A211737 A211739

Adjacent sequences: A250629 A250630 A250631 * A250633 A250634 A250635

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 26 2014

Status

approved