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 A296524 #26 Nov 23 2019 04:07:00 %S A296524 1,1,1,1,2,1,1,16,4,1,1,1,266,6,1,1,5,367860,10786,10,1,1,19,1 %N A296524 Number of connected (2*k)-regular graphs on 2*n+1 nodes with maximal diameter D(n,k) A294733 written as triangular array T(n,k), 1 <= k <= n. %C A296524 The next term a(24) corresponding to the 6-regular graphs on 15 nodes is conjectured to be 1. It seems that there exists only one graph with diameter A294733(24)=4. Its adjacency matrix is %C A296524 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 %C A296524 1 . 1 1 1 1 1 1 . . . . . . . . %C A296524 2 1 . 1 1 1 1 1 . . . . . . . . %C A296524 3 1 1 . 1 1 1 1 . . . . . . . . %C A296524 4 1 1 1 . 1 1 1 . . . . . . . . %C A296524 5 1 1 1 1 . 1 1 . . . . . . . . %C A296524 6 1 1 1 1 1 . . 1 . . . . . . . %C A296524 7 1 1 1 1 1 . . 1 . . . . . . . %C A296524 8 . . . . . 1 1 . 1 1 1 1 . . . %C A296524 9 . . . . . . . 1 . 1 1 . 1 1 1 %C A296524 10 . . . . . . . 1 1 . . 1 1 1 1 %C A296524 11 . . . . . . . 1 1 . . 1 1 1 1 %C A296524 12 . . . . . . . 1 . 1 1 . 1 1 1 %C A296524 13 . . . . . . . . 1 1 1 1 . 1 1 %C A296524 14 . . . . . . . . 1 1 1 1 1 . 1 %C A296524 15 . . . . . . . . 1 1 1 1 1 1 . %C A296524 The distance of 4 is achieved between nodes 1 and 13. None of the remaining 1470293674 graphs seems to have a diameter > 3. %C A296524 The conjecture is confirmed using Markus Meringer's GenReg program. Aside from the 1 shown 6-regular graph on 15 nodes with diameter 4 there are 870618932 graphs with diameter 2 and 599674742 graphs with diameter 3. - _Hugo Pfoertner_, Dec 19 2017 %D A296524 For references see A294733. %H A296524 M. Meringer, <a href="https://sourceforge.net/projects/genreg/">GenReg</a>, Generation of regular graphs. %e A296524 Degree r %e A296524 2 4 6 8 10 12 14 16 %e A296524 n -------------------------------------- %e A296524 3 | 1 Diameter A294733 %e A296524 | 1 Number of graphs with this diameter (this sequence) %e A296524 | %e A296524 5 | 2 1 %e A296524 | 1 1 %e A296524 | %e A296524 7 | 3 2 1 %e A296524 | 1 2 1 %e A296524 | %e A296524 9 | 4 2 2 1 %e A296524 | 1 16 4 1 %e A296524 | %e A296524 11 | 5 4 2 2 1 %e A296524 | 1 1 266 6 1 %e A296524 | %e A296524 13 | 6 5 2 2 2 1 %e A296524 | 1 5 367860 10786 10 1 %e A296524 | %e A296524 15 | 7 6 4 2 2 2 1 %e A296524 | 1 19 1 ? ? 17 1 %e A296524 | %e A296524 17 | 8 7 >=4 2 2 2 2 1 %e A296524 | 1 33 ? ? ? ? 25 1 %e A296524 . %e A296524 a(12)=1 corresponds to the only 4-regular graph on 11 nodes with diameter 4. %e A296524 Its adjacency matrix is %e A296524 . %e A296524 1 2 3 4 5 6 7 8 9 0 1 %e A296524 1 . 1 1 1 1 . . . . . . %e A296524 2 1 . 1 1 1 . . . . . . %e A296524 3 1 1 . 1 1 . . . . . . %e A296524 4 1 1 1 . . 1 . . . . . %e A296524 5 1 1 1 . . 1 . . . . . %e A296524 6 . . . 1 1 . 1 1 . . . %e A296524 7 . . . . . 1 . . 1 1 1 %e A296524 8 . . . . . 1 . . 1 1 1 %e A296524 9 . . . . . . 1 1 . 1 1 %e A296524 10 . . . . . . 1 1 1 . 1 %e A296524 11 . . . . . . 1 1 1 1 . %e A296524 . %e A296524 A shortest walk along 4 edges is required to reach node 9 from node 1. %e A296524 All others of the A068934(60)=265 4-regular graphs on 11 nodes have smaller diameters, i.e., 37 with diameter 2 and 227 with diameter 3. %Y A296524 Cf. A068934, A294733, A296525, A296526, A296620. %K A296524 nonn,tabl,hard,more %O A296524 1,5 %A A296524 _Hugo Pfoertner_, Dec 14 2017