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A348115 Irregular triangle read by rows: T(n, k) is the number of chains of subspaces 0 < V_1 < ... < V_r = (F_4)^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. 3
1, 1, 3, 1, 7, 24, 1, 12, 31, 117, 469, 1, 19, 111, 458, 1435, 6356, 28753, 1, 29, 361, 964, 1579, 15266, 55470, 71660, 264300, 1267174, 6105030, 1, 41, 1068, 8042, 4886, 145628, 494779, 1952843, 705790, 9589197, 38323695, 47157299, 188963325, 932529235 (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
FORMULA
If the k-th partition of n in A-St is L = (a, n-a), then T(n, k) = A347971(n, a) = A347971(n, n-a).
EXAMPLE
For L = (1, 1, 1), there are 105 (= 21 * 5) = A347487(3, 3) subspace chains 0 < V_1 < V_2 < (F_4)^3.
The permutations of the three coordinates classify them into 24 = T(3, 3) orbits.
T(3, 2) = 7 refers to partition (2, 1) and counts subspace chains in (F_4)^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 3
n=3: 1 7 24
n=4: 1 12 31 117 469
n=5: 1 19 111 458 1435 6356 28753
CROSSREFS
Sequence in context: A347485 A073676 A232149 * A282422 A282685 A194583
KEYWORD
nonn,tabf
AUTHOR
Álvar Ibeas, Oct 01 2021
STATUS
approved

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Last modified February 28 08:11 EST 2024. Contains 370393 sequences. (Running on oeis4.)