A252926 Number of n X 4 nonnegative integer arrays with upper left 0 and lower right n+4-6 and value increasing by 0 or 1 with every step right or down.

0, 1, 33, 615, 6997, 53950, 315198, 1499394, 6083808, 21733215, 69921908, 206052448, 563440284, 1444285973, 3499040581, 8065603025, 17787652381, 37705694442, 77126966988, 152747362302, 293741640632, 549886035657

Offset

1,3

Comments

Column 4 of A252930.

Links

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

Formula

Empirical: a(n) = (13/1609445376000)*n^16 + (13/18289152000)*n^15 + (3947/149448499200)*n^14 + (20057/37362124800)*n^13 + (728009/114960384000)*n^12 + (312437/7185024000)*n^11 + (1303193/7315660800)*n^10 + (848039/1828915200)*n^9 + (11500417/20901888000)*n^8 - (1346209/373248000)*n^7 - (14478857/1149603840)*n^6 - (361673/8164800)*n^5 + (13716552599/33530112000)*n^4 + (454863863/1397088000)*n^3 - (207327073/86486400)*n^2 + (137883/80080)*n.

Empirical: G.f.: x^2*(-1 -16*x -190*x^2 -350*x^3 +1419*x^4 -3792*x^5 +7860*x^6 -11238*x^7 +11247*x^8 -8133*x^9 +4280*x^10 -1600*x^11 +401*x^12 -60*x^13+4*x^14) / (x-1)^17. - R. J. Mathar, Nov 23 2015

Example

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

Crossrefs

Cf. A252930.

Sequence in context: A080597 A076684 A181382 * A225970 A004328 A235894

Adjacent sequences: A252923 A252924 A252925 * A252927 A252928 A252929

Keyword

nonn,changed

Author

R. H. Hardin, Dec 24 2014

Status

approved