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 A277444 #13 Feb 16 2025 08:33:36 %S A277444 0,0,2,0,0,6,0,2,0,12,0,0,42,24,20,0,2,48,420,120,30,0,0,306,2160, %T A277444 2420,360,42,0,2,600,17532,27600,9750,840,56,0,0,2442,115464,375260, %U A277444 191760,30702,1680,72,0,2,6048,830100,4810680,4098510,917280,81032,3024,90,0,0,20706,5745120,62813540,85691640,28669662,3406368,187560,5040,110 %N A277444 Square array A(n,k) (n>=1, k>=1) read by antidiagonals: A(n,k) is the number of n-colorings of the Möbius ladder M_k on 2k vertices. %C A277444 M_1 is two vertices connected by a triple edge and thus behaves like the path graph P_2 in terms of colorings. M_2 is isomorphic to K_4, the tetrahedral graph. %H A277444 N. L. Biggs, R. M. Damerell and D. A. Sands, <a href="https://dx.doi.org/10.1016%2F0095-8956%2872%2990016-0">Recursive families of graphs</a>, Journal of Combinatorial Theory Series B Volume 12 (1972), 123-131. MR0294172 %H A277444 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MoebiusLadder.html">Möbius Ladder</a> %H A277444 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">Chromatic polynomial</a> %F A277444 A(n,k) = (n^2-3n+3)^k+(n-1)((3-n)^k-(1-n)^k)-1. %e A277444 Square array A(n,k) begins: %e A277444 0, 0, 0, 0, 0, 0, 0, ... %e A277444 2, 0, 2, 0, 2, 0, 2, ... %e A277444 6, 0, 42, 48, 306, 600, 2442, ... %e A277444 12, 24, 420, 2160, 17532, 115464, 830100, ... %e A277444 20, 120, 2420, 27600, 375260, 4810680, 62813540, ... %e A277444 30, 360, 9750, 191760, 4098510, 85691640, 1801468230, ... %Y A277444 Cf. A277443 (colorings of prism graphs), A182406 (square grid graphs). %Y A277444 Columns k=1,2 are A002378 and A052762. Rows n=1,2 are A000004 and A010673. %K A277444 nonn,tabl %O A277444 1,3 %A A277444 _Jeremy Tan_, Oct 15 2016