This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A348180 #10 Oct 06 2021 19:19:29 %S A348180 1,1,4,1,9,40,1,19,56,279,1428,1,33,289,1561,6345,35689,202421,1,55, %T A348180 1358,4836,7652,129505,615395,757560,3620918,21341449,125952538,1,85, %U A348180 5771,80605,33435,2362185,10691648,53822709,14039541,321134138,1622410155,1916573757,9688635876,57866763847 %N 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. %C A348180 A permutation on the list of dimension increments does not modify the number of subspace chains. %C A348180 The length of the enumerated chains is r = len(L), where L is the parameter partition. %H A348180 Álvar Ibeas, <a href="/A348180/a348180.txt">First 16 rows, with gaps</a> %H A348180 Álvar Ibeas, <a href="/A348180/a348180_1.txt">Pseudo-column T(n, L), where L = (n-2, 1, 1), up to n=100</a> %H A348180 Álvar Ibeas, <a href="/A348180/a348180_2.txt">Pseudo-column T(n, L), where L = (n-3, 2, 1), up to n=100</a> %H A348180 Álvar Ibeas, <a href="/A348180/a348180_3.txt">Pseudo-column T(n, L), where L = (n-3, 1, 1, 1), up to n=100</a> %H A348180 Álvar Ibeas, <a href="/A348180/a348180_4.txt">Pseudo-column T(n, L), where L = (n-4, 3, 1), up to n=100</a> %H A348180 Álvar Ibeas, <a href="/A348180/a348180_5.txt">Pseudo-column T(n, L), where L = (n-4, 2, 2), up to n=100</a> %H A348180 Álvar Ibeas, <a href="/A348180/a348180_6.txt">Pseudo-column T(n, L), where L = (n-4, 2, 1, 1), up to n=100</a> %H A348180 Álvar Ibeas, <a href="/A348180/a348180_7.txt">Pseudo-column T(n, L), where L = (n-4, 1, 1, 1, 1), up to n=100</a> %F A348180 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). %e A348180 For L = (1, 1, 1), there are 186 (= 31 * 6) = A347488(3, 3) subspace chains 0 < V_1 < V_2 < (F_5)^3. %e A348180 The permutations of the three coordinates classify them into 40 = T(3, 3) orbits. %e A348180 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. %e A348180 Triangle begins: %e A348180 k: 1 2 3 4 5 6 7 %e A348180 ------------------------------- %e A348180 n=1: 1 %e A348180 n=2: 1 4 %e A348180 n=3: 1 9 40 %e A348180 n=4: 1 19 56 279 1428 %e A348180 n=5: 1 33 289 1561 6345 35689 202421 %Y A348180 Cf. A347972, A347488, A348113-A348115. %K A348180 nonn,tabf %O A348180 1,3 %A A348180 _Álvar Ibeas_, Oct 05 2021