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A347974

Triangle read by rows: T(n, k) is the number of k-dimensional subspaces in (F_8)^n, counted up to coordinate permutation (n >= 0, 0 <= k <= n).

1, 1, 1, 1, 5, 1, 1, 17, 17, 1, 1, 47, 242, 47, 1, 1, 113, 3071, 3071, 113, 1, 1, 245, 34477, 232290, 34477, 245, 1, 1, 491, 341633, 16665755, 16665755, 341633, 491, 1, 1, 920, 3022045, 1073874283, 8241549097, 1073874283, 3022045, 920, 1, 1, 1635, 24145695

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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

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

FORMULA

T(n, 1) = T(n - 1, 1) + A032192(n + 7).

EXAMPLE

Triangle begins:

k: 0 1 2 3 4 5

--------------------------

n=0: 1

n=1: 1 1

n=2: 1 5 1

n=3: 1 17 17 1

n=4: 1 47 242 47 1

n=5: 1 113 3071 3071 113 1

There are 9 = A022172(2, 1) one-dimensional subspaces in (F_8)^2. Among them, <(1, 1)> is invariant by coordinate swap and the rest are grouped in orbits of size two. Hence, T(2, 1) = 5.

CROSSREFS

Cf. A022172, A032192, A241926.

Sequence in context: A157637 A388426 A157181 * A029847 A154334 A178346

Adjacent sequences: A347971 A347972 A347973 * A347975 A347976 A347977

KEYWORD

nonn,tabl

AUTHOR

Álvar Ibeas, Sep 21 2021

STATUS

approved

URL: https://oeis.org/A347974

⇱ A347974 - OEIS