A347974 Triangle read by rows: T(n, k) is the number of k-dimensional subspaces in (F_8)^n, counted up to coordinate permutation (n >= 0, 0 <= k <= n).

1, 1, 1, 1, 5, 1, 1, 17, 17, 1, 1, 47, 242, 47, 1, 1, 113, 3071, 3071, 113, 1, 1, 245, 34477, 232290, 34477, 245, 1, 1, 491, 341633, 16665755, 16665755, 341633, 491, 1, 1, 920, 3022045, 1073874283, 8241549097, 1073874283, 3022045, 920, 1, 1, 1635, 24145695

Offset: 0

Author

Álvar Ibeas, Sep 21 2021

Keywords

• nonn
• tabl

Comments

Columns can be computed by a method analogous to that of Fripertinger for isometry classes of linear codes, disallowing scalar transformation of individual coordinates.

Regarding the formula for column k = 1, note that A241926(q - 1, n) counts, up to coordinate permutation, one-dimensional subspaces of (F_q)^n generated by a vector with no zero component.

Examples

			Triangle begins:
  k:  0    1    2    3    4    5
      --------------------------
n=0:  1
n=1:  1    1
n=2:  1    5    1
n=3:  1   17   17    1
n=4:  1   47  242   47    1
n=5:  1  113 3071 3071  113    1
There are 9 = A022172(2, 1) one-dimensional subspaces in (F_8)^2. Among them, <(1, 1)> is invariant by coordinate swap and the rest are grouped in orbits of size two. Hence, T(2, 1) = 5.
		

Links

• Álvar Ibeas, Entries up to T(10, 4)
• H. Fripertinger, Isometry classes of codes
• Álvar Ibeas, Column k=1 up to n=100
• Álvar Ibeas, Column k=2 up to n=100
• Álvar Ibeas, Column k=3 up to n=100
• Álvar Ibeas, Column k=4 up to n=100

Crossrefs

Cf. A022172, A032192, A241926.

Formula

T(n, 1) = T(n - 1, 1) + A032192(n + 7).