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A252876
T(n,k) = Number of n X k nonnegative integer arrays with upper left 0 and lower right n+k-4 and value increasing by 0 or 1 with every step right or down.
11
0, 0, 0, 1, 1, 1, 3, 8, 8, 3, 6, 26, 44, 26, 6, 10, 61, 153, 153, 61, 10, 15, 120, 413, 615, 413, 120, 15, 21, 211, 949, 1953, 1953, 949, 211, 21, 28, 343, 1948, 5281, 7313, 5281, 1948, 343, 28, 36, 526, 3676, 12686, 23203, 23203, 12686, 3676, 526, 36, 45, 771, 6497, 27805, 64920, 85801, 64920, 27805, 6497, 771, 45
OFFSET
1,7
COMMENTS
Table starts
..0...0.....1......3......6......10.......15........21........28.........36
..0...1.....8.....26.....61.....120......211.......343.......526........771
..1...8....44....153....413.....949.....1948......3676......6497......10894
..3..26...153....615...1953....5281....12686.....27805.....56624.....108549
..6..61...413...1953...7313...23203....64920....164399....383735.....836797
.10.120...949...5281..23203...85801...277585....806347...2142634....5281314
.15.211..1948..12686..64920..277585..1030330...3407823..10237249...28340232
.21.343..3676..27805.164399..806347..3407823..12742873..42993671..132872804
.28.526..6497..56624.383735.2142634.10237249..42993671.161937617..555632319
.36.771.10894.108549.836797.5281314.28340232.132872804.555632319.2105918045
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..2850 (first 479 terms from R. H. Hardin)
FORMULA
Empirical for column k:
k=1: a(n) = (1/2)*n^2 - (3/2)*n + 1
k=2: a(n) = (1/24)*n^4 + (5/12)*n^3 - (13/24)*n^2 - (11/12)*n + 1,
k=3: [polynomial of degree 6]
k=4: [polynomial of degree 8]
k=5: [polynomial of degree 10]
k=6: [polynomial of degree 12]
k=7: [polynomial of degree 14]
Empirical: with "n+k-3" instead of "n+k-4" T(n,k) = binomial(n+k,k) - 2.
EXAMPLE
Some solutions for n=3 k=4
..0..1..1..1....0..0..1..1....0..1..2..3....0..0..1..1....0..0..1..1
..1..1..2..2....0..1..1..2....1..1..2..3....0..0..1..2....0..1..2..2
..1..1..2..3....1..2..2..3....1..2..2..3....1..1..2..3....1..1..2..3
CROSSREFS
Columns 1-7 give: A000217(n-2), A252870, A252871, A252872, A252873, A252874, A252875.
Main diagonal is A252869.
Sequence in context: A301484 A249451 A019744 * A102639 A371941 A232182
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 24 2014
STATUS
approved