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.
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
Offset: 1
Examples
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
Links
- 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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