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 A277443 #15 Feb 16 2025 08:33:36 %S A277443 0,0,0,0,2,0,0,0,18,0,0,2,12,84,0,0,0,114,264,260,0,0,2,180,2652,1920, %T A277443 630,0,0,0,858,16080,29660,8520,1302,0,0,2,1932,119844,367080,198030, %U A277443 28140,2408,0,0,0,7074,816984,4843460,4067280,932862,76272,4104,0,0,2,18660,5784492,62682480,85847910,28576380,3440024,179424,6570,0 %N A277443 Square array A(n,k) (n>=1, k>=1) read by antidiagonals: A(n,k) is the number of n-colorings of the prism graph Y_k on 2k vertices. %C A277443 Y_1 contains a loop, so has no colorings with any number of colors. Y_2 is the cycle graph C_4 with two double edges; these two graphs are therefore equivalent with respect to number of colorings. %H A277443 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 A277443 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a> %H A277443 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">Chromatic polynomial</a> %F A277443 A(n,k) = (n^2-3n+3)^k+(n-1)((3-n)^k+(1-n)^k)+n^2-3n+1. %e A277443 Square array A(n,k) begins: %e A277443 0, 0, 0, 0, 0, 0, 0, ... %e A277443 0, 2, 0, 2, 0, 2, 0, ... %e A277443 0, 18, 12, 114, 180, 858, 1932, ... %e A277443 0, 84, 264, 2652, 16080, 119844, 816984, ... %e A277443 0, 260, 1920, 29660, 367080, 4843460, 62682480, ... %e A277443 0, 630, 8520, 198030, 4067280, 85847910, 1800687000, ... %Y A277443 Cf. A277444 (colorings of Möbius ladders), A182406 (square grid graphs). %Y A277443 Columns k=1,2 are A000004 and A091940. %Y A277443 Rows n=1,2 are A000004 and A010673. %K A277443 nonn,tabl %O A277443 1,5 %A A277443 _Jeremy Tan_, Oct 15 2016