A252925 Number of n X 3 nonnegative integer arrays with upper left 0 and lower right n+3-6 and value increasing by 0 or 1 with every step right or down.

0, 0, 1, 33, 413, 2859, 13976, 54199, 177848, 513905, 1342933, 3233784, 7275049, 15451358, 31234528, 60485192, 112793064, 203424686, 356097793, 606862907, 1009447181, 1642504781, 2619324320, 4100669333, 6311574992, 9563095895

Offset

1,4

Comments

Column 3 of A252930.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (1/59875200)*n^12 + (1/997920)*n^11 + (31/1360800)*n^10 + (1/5040)*n^9 + (79/453600)*n^8 - (71/15120)*n^7 - (4127/1360800)*n^6 + (319/9072)*n^5 + (52061/5443200)*n^4 - (2587/6048)*n^3 + (3315209/1663200)*n^2 - (11097/3080)*n + 2.

Empirical: G.f.: -x^3*(1 +20*x +62*x^2 -222*x^3 +300*x^4 -297*x^5 +255*x^6 -167*x^7 +72*x^8 -18*x^9 +2*x^10) / (x-1)^13. - R. J. Mathar, Nov 21 2015

Example

Some solutions for n=4:
..0..0..0....0..0..0....0..0..1....0..0..0....0..1..1....0..0..0....0..0..0
..0..1..1....0..0..0....0..0..1....0..0..1....1..1..1....0..0..0....0..1..1
..1..1..1....0..1..1....0..1..1....0..0..1....1..1..1....0..0..0....0..1..1
..1..1..1....1..1..1....0..1..1....0..0..1....1..1..1....0..0..1....0..1..1

Crossrefs

Sequence in context: A244502 A202256 A324950 * A107965 A220591 A296839

Adjacent sequences: A252922 A252923 A252924 * A252926 A252927 A252928

Keyword

nonn

Author

R. H. Hardin, Dec 24 2014

Status

approved