A377067 Number of n X 3 0..2 matrices with row sums 3 and column sums n up to permutations of rows.

1, 1, 4, 6, 12, 18, 30, 42, 63, 85, 118, 154, 204, 258, 330, 408, 507, 615, 748, 892, 1066, 1254, 1476, 1716, 1995, 2295, 2640, 3010, 3430, 3880, 4386, 4926, 5529, 6171, 6882, 7638, 8470, 9352, 10318, 11340, 12453, 13629, 14904, 16248, 17700, 19228, 20872, 22600, 24453, 26397, 28476

Offset: 0

Author

Andrew Howroyd, Oct 15 2024

Keywords

• nonn
• easy

Comments

Also, the number of n X 3 {-1,0,1} matrices with all rows and columns summing to zero up to permutations of rows.

Examples

			The a(2) = 4 matrices are:
  [1 1 1]  [2 1 0]  [2 0 1]  [1 2 0]
  [1 1 1]  [0 1 2]  [0 2 0]  [1 0 2]
The a(3) = 6 matrices are:
  [1 1 1]  [2 1 0]  [2 0 1]  [1 2 0]  [2 1 0]  [2 0 1]
  [1 1 1]  [0 1 2]  [0 2 0]  [1 0 2]  [1 0 2]  [1 2 0]
  [1 1 1]  [1 1 1]  [1 1 1]  [1 1 1]  [0 2 1]  [0 1 2]
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,1,-3,-1,1,3,-1,-2,1).

Crossrefs

Column k=3 of A377063.

Cf. A172634, A377065, A377068.

Programs

PARI

Vec((1 - x + x^2)/((1 - x)^5*(1 + x)^2*(1 + x + x^2)) + O(x^51))

Formula

G.f.: (2/(1 - x^3) - 1)/((1 - x)*(1 - x^2)^3).

G.f.: (1 - x + x^2)/((1 - x)^5*(1 + x)^2*(1 + x + x^2)).