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 A348115 #14 Oct 06 2021 12:19:09 %S A348115 1,1,3,1,7,24,1,12,31,117,469,1,19,111,458,1435,6356,28753,1,29,361, %T A348115 964,1579,15266,55470,71660,264300,1267174,6105030,1,41,1068,8042, %U A348115 4886,145628,494779,1952843,705790,9589197,38323695,47157299,188963325,932529235 %N 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. %C A348115 A permutation on the list of dimension increments does not modify the number of subspace chains. %C A348115 The length of the enumerated chains is r = len(L), where L is the parameter partition. %H A348115 Álvar Ibeas, <a href="/A348115/a348115.txt">First 16 rows, with gaps</a> %H A348115 Álvar Ibeas, <a href="/A348115/a348115_1.txt">Pseudo-column T(n, L), where L = (n-2, 1, 1), up to n=100</a> %H A348115 Álvar Ibeas, <a href="/A348115/a348115_2.txt">Pseudo-column T(n, L), where L = (n-3, 2, 1), up to n=100</a> %H A348115 Álvar Ibeas, <a href="/A348115/a348115_3.txt">Pseudo-column T(n, L), where L = (n-3, 1, 1, 1), up to n=100</a> %H A348115 Álvar Ibeas, <a href="/A348115/a348115_4.txt">Pseudo-column T(n, L), where L = (n-4, 3, 1), up to n=100</a> %H A348115 Álvar Ibeas, <a href="/A348115/a348115_5.txt">Pseudo-column T(n, L), where L = (n-4, 2, 2), up to n=100</a> %H A348115 Álvar Ibeas, <a href="/A348115/a348115_6.txt">Pseudo-column T(n, L), where L = (n-4, 2, 1, 1), up to n=100</a> %H A348115 Álvar Ibeas, <a href="/A348115/a348115_7.txt">Pseudo-column T(n, L), where L = (n-4, 1, 1, 1, 1), up to n=100</a> %F A348115 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). %e A348115 For L = (1, 1, 1), there are 105 (= 21 * 5) = A347487(3, 3) subspace chains 0 < V_1 < V_2 < (F_4)^3. %e A348115 The permutations of the three coordinates classify them into 24 = T(3, 3) orbits. %e A348115 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. %e A348115 Triangle begins: %e A348115 k: 1 2 3 4 5 6 7 %e A348115 ---------------------------- %e A348115 n=1: 1 %e A348115 n=2: 1 3 %e A348115 n=3: 1 7 24 %e A348115 n=4: 1 12 31 117 469 %e A348115 n=5: 1 19 111 458 1435 6356 28753 %Y A348115 Cf. A347971, A347487. %K A348115 nonn,tabf %O A348115 1,3 %A A348115 _Álvar Ibeas_, Oct 01 2021