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URL: https://oeis.org/A252930

⇱ A252930 - OEIS

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A252930
T(n,k) = Number of n X k nonnegative integer arrays with upper left 0 and lower right n+k-6 and value increasing by 0 or 1 with every step right or down.
10
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 5, 19, 33, 33, 19, 5, 15, 120, 413, 615, 413, 120, 15, 35, 483, 2859, 6997, 6997, 2859, 483, 35, 70, 1500, 13976, 53950, 84910, 53950, 13976, 1500, 70, 126, 3923, 54199, 315198, 762227, 762227, 315198, 54199, 3923, 126, 210
OFFSET
1,16
COMMENTS
Table starts
...0....0......0........0.........1...........5...........15............35
...0....0......0........1........19.........120..........483..........1500
...0....0......1.......33.......413........2859........13976.........54199
...0....1.....33......615......6997.......53950.......315198.......1499394
...1...19....413.....6997.....84910......762227......5385305......31454256
...5..120...2859....53950....762227.....8241540.....71297441.....512868867
..15..483..13976...315198...5385305....71297441....759337545....6725497344
..35.1500..54199..1499394..31454256...512868867...6725497344...73117894428
..70.3923.177848..6083808.157376166..3160111147..50869309436..675539536773
.126.9069.513905.21733215.692347393.17063990547.335549742230.5411459549576
FORMULA
Empirical for column k:
k=1: a(n) = (1/24)*n^4 - (5/12)*n^3 + (35/24)*n^2 - (25/12)*n + 1.
k=2: [polynomial of degree 8]
k=3: [polynomial of degree 12]
k=4: [polynomial of degree 16]
k=5: [polynomial of degree 20]
k=6: [polynomial of degree 24]
k=7: [polynomial of degree 28]
Empirical: with "n+k-3" instead of "n+k-6" T(n,k) = binomial(n+k,k) - 2.
EXAMPLE
Some solutions for n=4, k=4:
..0..1..1..1....0..0..0..0....0..0..0..0....0..1..1..2....0..0..0..1
..1..1..1..1....1..1..1..1....0..0..0..1....1..1..2..2....0..1..1..2
..1..1..2..2....1..1..1..1....1..1..1..1....1..1..2..2....0..1..1..2
..1..2..2..2....1..1..1..2....1..2..2..2....1..2..2..2....1..2..2..2
CROSSREFS
Column 1 is A000332(n-1), other columns are A252924 - A252929. Cf. A252923 (diagonal); A252876 (lower right n+k-4), A252976 (lower right n+k-5).
Sequence in context: A356716 A262700 A243269 * A031019 A324557 A255413
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 24 2014
STATUS
approved