A347973 Triangle read by rows: T(n, k) is the number of k-dimensional subspaces in (F_7)^n, counted up to coordinate permutation (n >= 0, 0 <= k <= n).

1, 1, 1, 1, 5, 1, 1, 15, 15, 1, 1, 37, 162, 37, 1, 1, 79, 1538, 1538, 79, 1, 1, 159, 13237, 74830, 13237, 159, 1, 1, 291, 102019, 3546909, 3546909, 102019, 291, 1, 1, 508, 708712, 153181682, 1010416196, 153181682, 708712, 508, 1, 1, 843, 4473998, 5954653026, 267444866627

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   15   15    1
n=4:  1   37  162   37    1
n=5:  1   79 1538 1538   79    1
There are 8 = A022171(2, 1) one-dimensional subspaces in (F_7)^2. Two of them (<(1, 1)> and <(1, 6)>) are invariant by coordinate swap, while 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. A022171, A032191, A241926.

Formula

T(n, 1) = T(n - 1, 1) + A032191(n + 6).