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

0,5

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.

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

Example

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.

Crossrefs

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

Sequence in context: A253670 A137897 A296327 * A296541 A056152 A171229

Adjacent sequences: A347967 A347968 A347969 * A347971 A347972 A347973

Keyword

nonn,tabl

Author

Álvar Ibeas, Sep 21 2021

Status

approved