A252873 Number of n X 5 nonnegative integer arrays with upper left 0 and lower right n+5-4 and value increasing by 0 or 1 with every step right or down.

6, 61, 413, 1953, 7313, 23203, 64920, 164399, 383735, 836797, 1722394, 3373453, 6327844, 11427851, 19956855, 33823579, 55806260, 89871373, 141584051, 218630137, 331472883, 494170691, 725385986, 1049619335, 1498707293

Offset

1,1

Comments

Column 5 of A252876.

Links

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

Formula

Empirical: a(n) = (1/259200)*n^10 + (1/6480)*n^9 + (149/60480)*n^8 + (163/7560)*n^7 + (10411/86400)*n^6 + (1027/2160)*n^5 + (16357/12960)*n^4 + (937/810)*n^3 + (1756/1575)*n^2 - (727/630)*n + 3.

Empirical: G.f.: -x*(6 -5*x +72*x^2 -225*x^3 +460*x^4 -612*x^5 +537*x^6 -315*x^7 +121*x^8 -28*x^9 +3*x^10) / (x-1)^11. - R. J. Mathar, Nov 21 2015

Example

Some solutions for n=3:
..0..1..2..3..4....0..0..0..1..2....0..1..1..1..2....0..0..1..1..2
..1..2..2..3..4....0..0..1..2..3....0..1..2..2..3....1..1..1..2..3
..2..3..3..4..4....0..1..2..3..4....1..2..3..3..4....1..1..2..3..4

Crossrefs

Sequence in context: A326739 A055331 A024523 * A068171 A069633 A069618

Adjacent sequences: A252870 A252871 A252872 * A252874 A252875 A252876

Keyword

nonn

Author

R. H. Hardin, Dec 24 2014

Status

approved