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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).
3
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.
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
KEYWORD
nonn,tabl
AUTHOR
Álvar Ibeas, Sep 21 2021
STATUS
approved