A202807 Number of n X 3 nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.

1, 6, 32, 121, 356, 881, 1925, 3830, 7083, 12352, 20526, 32759, 50518, 75635, 110363, 157436, 220133, 302346, 408652, 544389, 715736, 929797, 1194689, 1519634, 1915055, 2392676, 2965626, 3648547, 4457706, 5411111, 6528631, 7832120, 9345545

Offset: 1

Author

R. H. Hardin, Dec 24 2011

Keywords

• nonn

Comments

Column 3 of A202812.

Examples

			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    0 0 1    0 0 0    0 1 2    0 1 1    0 0 0
  0 1 2    0 0 1    0 0 1    0 0 0    0 1 2    0 1 1    0 0 2
  0 2 2    0 2 3    0 1 3    0 0 2    0 2 2    0 2 2    0 1 2
  0 2 4    0 2 3    0 2 4    0 1 3    0 2 2    0 2 2    0 2 2
		

Links

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

Crossrefs

Cf. A202812.

Formula

Empirical: a(n) = (1/180)*n^6 + (1/20)*n^5 + (13/72)*n^4 - (67/360)*n^2 + (19/20)*n.

Conjectures from Colin Barker, Jun 02 2018: (Start)

G.f.: x*(1 - x + 11*x^2 - 12*x^3 + 6*x^4 - x^5) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)