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 A296620 #11 Dec 17 2017 10:06:01 %S A296620 1,0,1,0,2,0,6,0,16,0,24,35,0,37,227,1,0,26,1502,16,0,10,10561,202,5, %T A296620 0,1,84103,4006,58,0,1,722252,82726,493,19,0,0,6383913,1647078,6224, %U A296620 202,1,0,0,55831405,30291536,96504,2156,33 %N A296620 Number of 4-regular (quartic) connected graphs on n nodes with diameter k written as irregular triangle T(n,k). %C A296620 The results were found by applying the Floyd-Warshall algorithm to the output of Markus Meringer's GenReg program. %H A296620 M. Meringer, <a href="https://sourceforge.net/projects/genreg/">GenReg</a>, Generation of regular graphs. %H A296620 Wikipedia, <a href="https://en.wikipedia.org/wiki/Distance_(graph_theory)">Distance (graph theory).</a> %H A296620 Wikipedia, <a href="https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm">Floyd-Warshall algorithm.</a> %e A296620 Triangle begins: %e A296620 Diameter %e A296620 n/ 1 2 3 4 5 6 7 %e A296620 5: 1 %e A296620 6: 0 1 %e A296620 7: 0 2 %e A296620 8: 0 6 %e A296620 9: 0 16 %e A296620 10: 0 24 35 %e A296620 11: 0 37 227 1x %e A296620 12: 0 26 1502 16 %e A296620 13: 0 10 10561 202 5 %e A296620 14: 0 1x 84103 4006 58 %e A296620 15: 0 1x 722252 82726 493 19 %e A296620 16: 0 0 6383913 1647078 6224 202 1x %e A296620 17: 0 0 55831405 30291536 96504 2156 33 %e A296620 . %e A296620 x indicates provision of adjacency information below. %e A296620 Examples of unique 4-regular graphs with minimum diameter: %e A296620 Adjacency matrix of the graph of diameter 2 on 14 nodes: %e A296620 1 2 3 4 5 6 7 8 9 0 1 2 3 4 %e A296620 1 . 1 1 1 1 . . . . . . . . . %e A296620 2 1 . . . . 1 1 1 . . . . . . %e A296620 3 1 . . . . 1 1 1 . . . . . . %e A296620 4 1 . . . . . . . 1 1 1 . . . %e A296620 5 1 . . . . . . . . . . 1 1 1 %e A296620 6 . 1 1 . . . . . 1 . . 1 . . %e A296620 7 . 1 1 . . . . . . 1 . . 1 . %e A296620 8 . 1 1 . . . . . . . 1 . . 1 %e A296620 9 . . . 1 . 1 . . . . . . 1 1 %e A296620 10 . . . 1 . . 1 . . . . 1 . 1 %e A296620 11 . . . 1 . . . 1 . . . 1 1 . %e A296620 12 . . . . 1 1 . . . 1 1 . . . %e A296620 13 . . . . 1 . 1 . 1 . 1 . . . %e A296620 14 . . . . 1 . . 1 1 1 . . . . %e A296620 . %e A296620 Adjacency matrix of the graph of diameter 2 on 15 nodes: %e A296620 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 %e A296620 1 . 1 1 1 1 . . . . . . . . . . %e A296620 2 1 . 1 . . 1 1 . . . . . . . . %e A296620 3 1 1 . . . . . 1 1 . . . . . . %e A296620 4 1 . . . . . . . . 1 1 1 . . . %e A296620 5 1 . . . . . . . . . . . 1 1 1 %e A296620 6 . 1 . . . . . . . 1 1 . 1 . . %e A296620 7 . 1 . . . . . . . . . 1 . 1 1 %e A296620 8 . . 1 . . . . . . 1 . 1 . 1 . %e A296620 9 . . 1 . . . . . . . 1 . 1 . 1 %e A296620 10 . . . 1 . 1 . 1 . . . . . . 1 %e A296620 11 . . . 1 . 1 . . 1 . . . . 1 . %e A296620 12 . . . 1 . . 1 1 . . . . 1 . . %e A296620 13 . . . . 1 1 . . 1 . . 1 . . . %e A296620 14 . . . . 1 . 1 1 . . 1 . . . . %e A296620 15 . . . . 1 . 1 . 1 1 . . . . . %e A296620 . %e A296620 Examples of unique graphs with maximum diameter: %e A296620 Adjacency matrix of the graph of diameter 4 on 11 nodes: %e A296620 1 2 3 4 5 6 7 8 9 0 1 %e A296620 1 . 1 1 1 1 . . . . . . %e A296620 2 1 . 1 1 1 . . . . . . %e A296620 3 1 1 . 1 1 . . . . . . %e A296620 4 1 1 1 . . 1 . . . . . %e A296620 5 1 1 1 . . 1 . . . . . %e A296620 6 . . . 1 1 . 1 1 . . . %e A296620 7 . . . . . 1 . . 1 1 1 %e A296620 8 . . . . . 1 . . 1 1 1 %e A296620 9 . . . . . . 1 1 . 1 1 %e A296620 10 . . . . . . 1 1 1 . 1 %e A296620 11 . . . . . . 1 1 1 1 . %e A296620 . %e A296620 Adjacency matrix of the graph of diameter 7 on 16 nodes: %e A296620 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 %e A296620 1 . 1 1 1 1 . . . . . . . . . . . %e A296620 2 1 . 1 1 1 . . . . . . . . . . . %e A296620 3 1 1 . 1 1 . . . . . . . . . . . %e A296620 4 1 1 1 . . 1 . . . . . . . . . . %e A296620 5 1 1 1 . . 1 . . . . . . . . . . %e A296620 6 . . . 1 1 . 1 1 . . . . . . . . %e A296620 7 . . . . . 1 . 1 1 1 . . . . . . %e A296620 8 . . . . . 1 1 . 1 1 . . . . . . %e A296620 9 . . . . . . 1 1 . 1 1 . . . . . %e A296620 10 . . . . . . 1 1 1 . 1 . . . . . %e A296620 11 . . . . . . . . 1 1 . 1 1 . . . %e A296620 12 . . . . . . . . . . 1 . . 1 1 1 %e A296620 13 . . . . . . . . . . 1 . . 1 1 1 %e A296620 14 . . . . . . . . . . . 1 1 . 1 1 %e A296620 15 . . . . . . . . . . . 1 1 1 . 1 %e A296620 16 . . . . . . . . . . . 1 1 1 1 . %Y A296620 Cf. A006820 (row sums), A204329, A294733 (number of terms in each row for odd n), A296525 (number of terms in each row for even n). %K A296620 nonn,tabf %O A296620 5,5 %A A296620 _Hugo Pfoertner_, Dec 17 2017