A252971 Number of nX3 nonnegative integer arrays with upper left 0 and lower right n+3-5 and value increasing by 0 or 1 with every step right or down.

0, 1, 18, 153, 770, 2859, 8694, 22924, 54272, 118057, 239798, 460207, 841930, 1478451, 2505634, 4116442, 6579440, 10261761, 15657290, 23420901, 34409666, 49732043, 70806142, 99428264, 137853008, 188886345, 255993166, 343420923

Offset

1,3

Comments

Column 3 of A252976.

Links

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

Formula

Empirical: a(n) = (1/90720)*n^9 + (1/2520)*n^8 + (19/3780)*n^7 + (7/360)*n^6 - (59/4320)*n^5 - (19/180)*n^4 + (5827/45360)*n^3 - (32/35)*n^2 + (3629/1260)*n - 2.

Empirical: G.f.: x^2*(1+8*x+18*x^2-70*x^3+94*x^4-78*x^5+43*x^6-14*x^7+2*x^8) / (x-1)^10. - R. J. Mathar, Nov 23 2015

Example

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

Crossrefs

Sequence in context: A294486 A228994 A235397 * A047643 A010934 A022613

Adjacent sequences: A252968 A252969 A252970 * A252972 A252973 A252974

Keyword

nonn

Author

R. H. Hardin, Dec 25 2014

Status

approved