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 A182797 #25 Aug 01 2023 14:18:32 %S A182797 1,0,2,0,0,3,0,0,6,4,0,0,6,24,5,0,0,6,192,60,6,0,0,6,2112,1620,120,7, %T A182797 0,0,6,32640,98820,7680,210,8,0,0,6,718080,13638780,1574400,26250,336, %U A182797 9,0,0,6,22665216,4260983940,1034019840,13676250,72576,504,10 %N A182797 Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) is the number of n-colorings of the k X k X k triangular grid. %C A182797 The k X k X k triangular grid has k rows with i vertices in row i. Each vertex is connected to the neighbors in the same row and up to two vertices in each of the neighboring rows. The graph has A000217(k) vertices and 3*A000217(k-1) edges altogether. %C A182797 The coefficients of the chromatic polynomials for the column sequences are given by the rows of A193283. - _Georg Fischer_, Jul 31 2023 %H A182797 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lattice_graph#Other_kinds">Triangular grid graph</a> %H A182797 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">Chromatic polynomial</a> %e A182797 Square array A(n,k) begins: %e A182797 1, 0, 0, 0, 0, 0, ... %e A182797 2, 0, 0, 0, 0, 0, ... %e A182797 3, 6, 6, 6, 6, 6, ... %e A182797 4, 24, 192, 2112, 32640, 718080, ... %e A182797 5, 60, 1620, 98820, 13638780, 4260983940, ... %e A182797 6, 120, 7680, 1574400, 1034019840, 2175789895680, ... %Y A182797 Columns k=1-11 give: A000027, A007531, A182788, A182789, A182790, A182791, A182792, A182793, A182794, A182795, A182796. %Y A182797 Rows n=1-10 give: A000007(k-1), A000038(k-1), A040006(k-1), A182798, A153467*4, A153468*5, A153469*6, A153470*7, A153471*8, A153472*9, A153473*10. %Y A182797 Cf. A000217, A193283. %K A182797 nonn,tabl %O A182797 1,3 %A A182797 _Alois P. Heinz_, Dec 02 2010