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 A384380 #7 Jun 01 2025 16:38:33 %S A384380 2,2,3,2,1,2,2,3,3,2,1,4,4,9,14,14,9,4,1,4,4,12,20,32,30,23,11,4,1,4, %T A384380 4,13,29,54,75,75,55,31,12,4,1,5,5,17,43,118,285,595,992,1320,1348, %U A384380 1045,603,262,86,22,5,1,3,4,6,7,6,3,1,3,4,7,12,17,16,9,3,1 %N A384380 Irregular triangle read by rows: T(n,k) is the number of connected subsets of k faces (or polyforms) of the n-th Johnson solid, up to symmetries of that solid; 1 <= n <= 92, 1 <= k <= A242731(n). %C A384380 Two faces are connected if they share an edge. %C A384380 Equivalently, T(n,k) is the number of connected induced k-vertex subgraphs of the 1-skeleton of the dual of the n-th Johnson solid, up to symmetries of that dual. %H A384380 Pontus von Brömssen, <a href="/A384380/b384380.txt">Table of n, a(n) for n = 1..341</a> (first 24 rows) %H A384380 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JohnsonSolid.html">Johnson Solid</a>. %H A384380 Wikipedia, <a href="https://en.wikipedia.org/wiki/List_of_Johnson_solids">List of Johnson solids</a>. %e A384380 Triangle begins: %e A384380 n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 %e A384380 ---+---------------------------------------------------------------------- %e A384380 1 | 2 2 3 2 1 %e A384380 2 | 2 2 3 3 2 1 %e A384380 3 | 4 4 9 14 14 9 4 1 %e A384380 4 | 4 4 12 20 32 30 23 11 4 1 %e A384380 5 | 4 4 13 29 54 75 75 55 31 12 4 1 %e A384380 6 | 5 5 17 43 118 285 595 992 1320 1348 1045 603 262 86 22 5 1 %e A384380 7 | 3 4 6 7 6 3 1 %e A384380 8 | 3 4 7 12 17 16 9 3 1 %e A384380 9 | 3 4 7 13 24 35 36 22 9 3 1 %e A384380 10 | 4 4 8 15 28 47 81 102 87 45 16 4 1 %e A384380 11 | 4 4 8 17 35 71 139 252 378 429 340 183 67 18 4 1 %e A384380 12 | 1 2 2 3 1 1 %e A384380 13 | 1 2 2 5 6 10 7 5 1 1 %e A384380 14 | 2 3 5 7 10 9 6 2 1 %e A384380 15 | 2 3 5 11 19 31 38 38 20 10 2 1 %e A384380 16 | 2 3 5 11 23 45 82 126 154 130 77 30 10 2 1 %e A384380 17 | 2 3 4 10 16 35 61 120 180 237 194 117 40 13 2 1 %e A384380 18 | 6 7 17 36 81 165 300 386 337 197 82 25 6 1 %e A384380 19 | 6 7 20 44 121 290 701 1403 2359 3047 2975 2110 1106 435 131 31 6 1 %Y A384380 Cf. A242731 (row lengths), A384376, A384378, A384381 (row sums). %K A384380 nonn,tabf,fini %O A384380 1,1 %A A384380 _Pontus von Brömssen_ and _Peter Kagey_, May 28 2025