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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
16
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 26 2014
STATUS
approved