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 A348114 #12 Oct 06 2021 12:18:54 %S A348114 1,1,3,1,5,15,1,8,16,49,154,1,11,39,126,288,964,3275,1,15,87,168,291, %T A348114 1412,3600,4957,12865,46400,168862,1,19,176,644,608,6101,14001,38996, %U A348114 22294,146064,418072,549894,1586761,6045724,23115063,1,24,338,2348,4849,1195,24329 %N 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. %C A348114 A permutation on the list of dimension increments does not modify the number of subspace chains. %C A348114 The length of the enumerated chains is r = len(L), where L is the parameter partition. %H A348114 Álvar Ibeas, <a href="/A348114/b348114.txt">Table of n, a(n) for n = 1..65</a> %H A348114 Álvar Ibeas, <a href="/A348114/a348114.txt">First 16 rows, with gaps</a> %H A348114 Álvar Ibeas, <a href="/A348114/a348114_1.txt">Pseudo-column T(n, L), where L = (n-2, 1, 1), up to n=100</a> %H A348114 Álvar Ibeas, <a href="/A348114/a348114_2.txt">Pseudo-column T(n, L), where L = (n-3, 2, 1), up to n=100</a> %H A348114 Álvar Ibeas, <a href="/A348114/a348114_3.txt">Pseudo-column T(n, L), where L = (n-3, 1, 1, 1), up to n=100</a> %H A348114 Álvar Ibeas, <a href="/A348114/a348114_4.txt">Pseudo-column T(n, L), where L = (n-4, 3, 1), up to n=100</a> %H A348114 Álvar Ibeas, <a href="/A348114/a348114_5.txt">Pseudo-column T(n, L), where L = (n-4, 2, 2), up to n=100</a> %H A348114 Álvar Ibeas, <a href="/A348114/a348114_6.txt">Pseudo-column T(n, L), where L = (n-4, 2, 1, 1), up to n=100</a> %H A348114 Álvar Ibeas, <a href="/A348114/a348114_7.txt">Pseudo-column T(n, L), where L = (n-4, 1, 1, 1, 1), up to n=100</a> %F A348114 If the k-th partition of n in A-St is L = (a, n-a), then T(n, k) = A347970(n, a) = A347970(n, n-a). %e A348114 For L = (1, 1, 1), there are 52 (= 13 * 4) = A347486(3, 3) subspace chains 0 < V_1 < V_2 < (F_3)^3. %e A348114 The permutations of the three coordinates classify them into 15 = T(3, 3) orbits. %e A348114 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. %e A348114 Triangle begins: %e A348114 k: 1 2 3 4 5 6 7 %e A348114 ------------------------ %e A348114 n=1: 1 %e A348114 n=2: 1 3 %e A348114 n=3: 1 5 15 %e A348114 n=4: 1 8 16 49 154 %e A348114 n=5: 1 11 39 126 288 964 3275 %Y A348114 Cf. A347970, A347486. %K A348114 nonn,tabf %O A348114 1,3 %A A348114 _Álvar Ibeas_, Oct 01 2021