A348114 Irregular triangle read by rows: T(n, k) is the number of chains of subspaces 0 < V_1 < ... < V_r = (F_3)^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.
1, 1, 3, 1, 5, 15, 1, 8, 16, 49, 154, 1, 11, 39, 126, 288, 964, 3275, 1, 15, 87, 168, 291, 1412, 3600, 4957, 12865, 46400, 168862, 1, 19, 176, 644, 608, 6101, 14001, 38996, 22294, 146064, 418072, 549894, 1586761, 6045724, 23115063, 1, 24, 338, 2348, 4849, 1195, 24329
Offset: 1
Examples
For L = (1, 1, 1), there are 52 (= 13 * 4) = A347486(3, 3) subspace chains 0 < V_1 < V_2 < (F_3)^3.
The permutations of the three coordinates classify them into 15 = T(3, 3) orbits.
T(3, 2) = 5 refers to partition (2, 1) and counts subspace chains in (F_3)^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 5 15
n=4: 1 8 16 49 154
n=5: 1 11 39 126 288 964 3275
Links
- Álvar Ibeas, Table of n, a(n) for n = 1..65
- 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
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