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 A193233 #22 Feb 16 2025 08:33:15 %S A193233 1,-3,2,0,1,-12,63,-190,363,-455,370,-180,40,0,1,-39,732,-8806,76293, %T A193233 -507084,2689452,-11689056,42424338,-130362394,342624075,-776022242, %U A193233 1522861581,-2598606825,3863562996,-5007519752,5652058863,-5541107684,4697231261 %N A193233 Triangle T(n,k), n>=1, 0<=k<=3^n, read by rows: row n gives the coefficients of the chromatic polynomial of the Hanoi graph H_n, highest powers first. %C A193233 The Hanoi graph H_n has 3^n vertices and 3*(3^n-1)/2 edges. It represents the states and allowed moves in the Towers of Hanoi problem with n disks. The chromatic polynomial of H_n has 3^n+1 coefficients. %H A193233 Alois P. Heinz, <a href="/A193233/b193233.txt">Rows n = 1..6, flattened</a> %H A193233 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a> %H A193233 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HanoiGraph.html">Hanoi Graph</a> %H A193233 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">Chromatic Polynomial</a> %H A193233 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tower_of_Hanoi">Tower of Hanoi</a> %e A193233 2 example graphs: o %e A193233 . / \ %e A193233 . o---o %e A193233 . / \ %e A193233 . o o o %e A193233 . / \ / \ / \ %e A193233 . o---o o---o---o---o %e A193233 Graph: H_1 H_2 %e A193233 Vertices: 3 9 %e A193233 Edges: 3 12 %e A193233 The Hanoi graph H_1 equals the cycle graph C_3 with chromatic polynomial %e A193233 q^3 -3*q^2 +2*q => [1, -3, 2, 0]. %e A193233 Triangle T(n,k) begins: %e A193233 1, -3, 2, 0; %e A193233 1, -12, 63, -190, 363, -455, ... %e A193233 1, -39, 732, -8806, 76293, -507084, ... %e A193233 1, -120, 7113, -277654, 8028540, -183411999, ... %e A193233 1, -363, 65622, -7877020, 706303350, -50461570575, ... %e A193233 1, -1092, 595443, -216167710, 58779577593, -12769539913071, ... %e A193233 ... %Y A193233 Cf. A000244, A029858. %Y A193233 Cf. A288839 (chromatic polynomials of the n-Hanoi graph). %Y A193233 Cf. A137889 (directed Hamiltonian paths in the n-Hanoi graph). %Y A193233 Cf. A288490 (independent vertex sets in the n-Hanoi graph). %Y A193233 Cf. A286017 (matchings in the n-Hanoi graph). %Y A193233 Cf. A193136 (spanning trees of the n-Hanoi graph). %Y A193233 Cf. A288796 (undirected paths in the n-Hanoi graph). %K A193233 sign,tabf,look,hard %O A193233 1,2 %A A193233 _Alois P. Heinz_, Jul 18 2011