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
Keywords
Examples
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
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
Comments