A202754 Number of n X 6 nonnegative integer arrays with each row and column increasing from zero by 0 or 1.

1, 6, 51, 462, 3809, 26394, 150777, 721382, 2964632, 10720688, 34811491, 103179440, 282848319, 724794396, 1751160378, 4017593748, 8804203831, 18519925138, 37551252015, 73653037370, 140173677721, 259538952486, 468599962315

Offset

1,2

Comments

Column 6 of A202756.

Links

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

Robert Israel, Maple-assisted proof of empirical formula

Formula

Empirical: a(n) = (1/4572288000)*n^15 + (1/76204800)*n^14 + (41/130636800)*n^13 + (1/272160)*n^12 + (12631/653184000)*n^11 + (113/5443200)*n^10 + (2941/914457600)*n^9 + (661/381024)*n^8 + (1820467/326592000)*n^7 - (38281/10886400)*n^6 + (995867/16329600)*n^5 + (4181/68040)*n^4 - (253877/2646000)*n^3 + (233011/529200)*n^2 + (667/1260)*n.

Empirical formula verified (see link). - Robert Israel, Jun 02 2019

Example

Some solutions for n=5:
  0 0 0 0 0 0   0 0 0 0 0 0   0 0 0 0 0 0   0 0 0 0 0 0
  0 0 1 1 1 1   0 0 0 1 1 1   0 0 0 0 0 0   0 0 0 1 1 1
  0 0 1 1 2 2   0 0 0 1 2 2   0 0 0 0 1 1   0 0 0 1 1 2
  0 0 1 1 2 2   0 0 0 1 2 3   0 0 1 1 1 2   0 0 1 2 2 3
  0 1 2 2 2 2   0 0 1 2 3 3   0 1 2 2 2 3   0 1 2 3 3 4

Maple

seq((1/4572288000)*n^15 + (1/76204800)*n^14 + (41/130636800)*n^13 + (1/272160)*n^12 + (12631/653184000)*n^11 + (113/5443200)*n^10 + (2941/914457600)*n^9 + (661/381024)*n^8 + (1820467/326592000)*n^7 - (38281/10886400)*n^6 + (995867/16329600)*n^5 + (4181/68040)*n^4 - (253877/2646000)*n^3 + (233011/529200)*n^2 + (667/1260)*n, n=1..30); # Robert Israel, Jun 02 2019

Crossrefs

Sequence in context: A292840 A356394 A377233 * A363112 A180901 A199685

Adjacent sequences: A202751 A202752 A202753 * A202755 A202756 A202757

Keyword

nonn

Author

R. H. Hardin, Dec 23 2011

Status

approved