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A348180 Irregular triangle read by rows: T(n, k) is the number of chains of subspaces 0 < V_1 < ... < V_r = (F_5)^n, counted up to coordinate permutation, with dimension increments given by (any fixed permutation of) the parts of the k-th partition of n in Abramowitz-Stegun order. 2
1, 1, 4, 1, 9, 40, 1, 19, 56, 279, 1428, 1, 33, 289, 1561, 6345, 35689, 202421, 1, 55, 1358, 4836, 7652, 129505, 615395, 757560, 3620918, 21341449, 125952538, 1, 85, 5771, 80605, 33435, 2362185, 10691648, 53822709, 14039541, 321134138, 1622410155, 1916573757, 9688635876, 57866763847 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A permutation on the list of dimension increments does not modify the number of subspace chains.

The length of the enumerated chains is r = len(L), where L is the parameter partition.

LINKS

Table of n, a(n) for n=1..43.

Álvar Ibeas, First 16 rows, with gaps

Álvar Ibeas, Pseudo-column T(n, L), where L = (n-2, 1, 1), up to n=100

Álvar Ibeas, Pseudo-column T(n, L), where L = (n-3, 2, 1), up to n=100

Álvar Ibeas, Pseudo-column T(n, L), where L = (n-3, 1, 1, 1), up to n=100

Álvar Ibeas, Pseudo-column T(n, L), where L = (n-4, 3, 1), up to n=100

Álvar Ibeas, Pseudo-column T(n, L), where L = (n-4, 2, 2), up to n=100

Álvar Ibeas, Pseudo-column T(n, L), where L = (n-4, 2, 1, 1), up to n=100

Álvar Ibeas, Pseudo-column T(n, L), where L = (n-4, 1, 1, 1, 1), up to n=100

FORMULA

If the k-th partition of n in A-St is L = (a, n-a), then T(n, k) = A347972(n, a) = A347972(n, n-a).

EXAMPLE

For L = (1, 1, 1), there are 186 (= 31 * 6) = A347488(3, 3) subspace chains 0 < V_1 < V_2 < (F_5)^3.

The permutations of the three coordinates classify them into 40 = T(3, 3) orbits.

T(3, 2) = 9 refers to partition (2, 1) and counts subspace chains in (F_5)^2 with dimensions (0, 2, 3), i.e. 2-dimensional subspaces. It also counts chains with dimensions (0, 1, 3), i.e. 1-dimensional subspaces.

Triangle begins:

  k:  1  2   3    4    5     6      7

      -------------------------------

n=1:  1

n=2:  1  4

n=3:  1  9  40

n=4:  1 19  56  279 1428

n=5:  1 33 289 1561 6345 35689 202421

CROSSREFS

Cf. A347972, A347488, A348113-A348115.

Sequence in context: A128626 A193963 A028941 * A176080 A328302 A346748

Adjacent sequences:  A348177 A348178 A348179 * A348181 A348182 A348183

KEYWORD

nonn,tabf

AUTHOR

Álvar Ibeas, Oct 05 2021

STATUS

approved

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Last modified January 18 20:41 EST 2022. Contains 350455 sequences. (Running on oeis4.)