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
Keywords
Examples
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
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
Comments