Voozh

A347972

Triangle read by rows: T(n, k) is the number of k-dimensional subspaces in (F_5)^n, counted up to coordinate permutation (n >= 0, 0 <= k <= n).

1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 19, 56, 19, 1, 1, 33, 289, 289, 33, 1, 1, 55, 1358, 4836, 1358, 55, 1, 1, 85, 5771, 80605, 80605, 5771, 85, 1, 1, 128, 22594, 1271870, 5525686, 1271870, 22594, 128, 1, 1, 183, 81802, 18478460, 372302962, 372302962, 18478460, 81802, 183, 1

(list; table; graph; refs; listen; history; text; internal format)

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(12, 5)

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

Álvar Ibeas, Column k=5 up to n=100

FORMULA

T(n, 1) = T(n - 1, 1) + A008610(n).

EXAMPLE

Triangle begins:

k: 0 1 2 3 4 5 6

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

n=0: 1

n=1: 1 1

n=2: 1 4 1

n=3: 1 9 9 1

n=4: 1 19 56 19 1

n=5: 1 33 289 289 33 1

n=6: 1 55 1358 4836 1358 55 1

There are 6 = A022169(2, 1) one-dimensional subspaces in (F_5)^2. By coordinate swap, <(0, 1)> is identified with <(1, 0)> and <(1, 2)> with <(1, 3)>, while <(1, 1)> and <(1, 4)> rest invariant. Hence, T(2, 1) = 4.

CROSSREFS

Cf. A022169, A008610, A241926.

Sequence in context: A180960 A157192 A154982 * A146767 A146955 A155451

Adjacent sequences: A347969 A347970 A347971 * A347973 A347974 A347975

KEYWORD

nonn,tabl

AUTHOR

Álvar Ibeas, Sep 21 2021

STATUS

approved

URL: https://oeis.org/A347972

⇱ A347972 - OEIS