A347970 Triangle read by rows: T(n, k) is the number of k-dimensional subspaces in (F_3)^n, counted up to coordinate permutation (n >= 0, 0 <= k <= n).

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 8, 16, 8, 1, 1, 11, 39, 39, 11, 1, 1, 15, 87, 168, 87, 15, 1, 1, 19, 176, 644, 644, 176, 19, 1, 1, 24, 338, 2348, 4849, 2348, 338, 24, 1, 1, 29, 613, 8137, 37159, 37159, 8137, 613, 29, 1, 1, 35, 1071, 27047, 286747, 679054, 286747, 27047, 1071

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.

Examples

			Triangle begins:
  k:  0   1   2   3   4   5   6   7
      -----------------------------
n=0:  1
n=1:  1   1
n=2:  1   3   1
n=3:  1   5   5   1
n=4:  1   8  16   8   1
n=5:  1  11  39  39  11   1
n=6:  1  15  87 168  87  15   1
n=7:  1  19 176 644 644 176  19   1
There are 4 = A022167(2, 1) one-dimensional subspaces in (F_3)^2, namely, those generated by (0, 1), (1, 0), (1, 1), and (1, 2). The first two are related by coordinate swap, while the remaining two are invariant. Hence, T(2, 1) = 3.
		

Links

• Álvar Ibeas, Entries up to T(16, 7)
• H. Fripertinger, Isometry classes of codes
• H. Fripertinger, Number of the isometry classes of all ternary (n,k)-codes
• 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
• Álvar Ibeas, Column k=5 up to n=100
• Álvar Ibeas, Column k=6 up to n=100
• Álvar Ibeas, Column k=7 up to n=100

Crossrefs

Cf. A022167, A024206(n+1) (column k=1), A076831.