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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).
2
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
0,5
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.
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.
LINKS
H. Fripertinger, Isometry classes of codes
FORMULA
T(n, 1) = T(n-1, 1) + A032193(n+8).
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Álvar Ibeas, Sep 21 2021
STATUS
approved