A347975 Triangle read by rows: T(n, k) is the number of k-dimensional subspaces in (F_9)^n, counted up to coordinate permutation (n >= 0, 0 <= k <= n).

1, 1, 1, 1, 6, 1, 1, 21, 21, 1, 1, 64, 374, 64, 1, 1, 163, 5900, 5900, 163, 1, 1, 380, 82587, 644680, 82587, 380, 1, 1, 809, 1018388, 66136870, 66136870, 1018388, 809, 1, 1, 1619, 11174165, 6057912073, 52901629980, 6057912073, 11174165, 1619, 1, 1, 3049, 110404788

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    6    1
n=3:  1   21   21    1
n=4:  1   64  374   64    1
n=5:  1  163 5900 5900  163    1
There are 10 = A022173(2, 1) one-dimensional subspaces in (F_9)^2. Among them, <(1, 1)> and <(1, 2)> are invariant by coordinate swap and the rest are grouped in orbits of size two. Hence, T(2, 1) = 6.
		

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. A022173, A032193, A241926.

Formula

T(n, 1) = T(n-1, 1) + A032193(n+8).