cp's OEIS Frontend

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.

A184963 Number of connected 6-regular simple graphs on n vertices with girth exactly 3.

This page as a plain text file.
%I A184963 #16 Jan 27 2020 03:55:44
%S A184963 0,0,0,0,0,0,0,1,1,4,21,266,7848,367860,21609299,1470293674,
%T A184963 113314233799,9799685588930
%N A184963 Number of connected 6-regular simple graphs on n vertices with girth exactly 3.
%H A184963 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_eq_g_index">Index of sequences counting connected k-regular simple graphs with girth exactly g</a>
%F A184963 a(n) = A006822(n) - A058276(n).
%e A184963 a(0)=0 because even though the null graph (on zero vertices) is vacuously 6-regular and connected, since it is acyclic, it has infinite girth.
%e A184963 The a(7)=1 complete graph on 7 vertices is 6-regular; it has 21 edges and 35 triangles.
%t A184963 A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];
%t A184963 A006822 = A@006822;
%t A184963 A058276 = A@058276;
%t A184963 a[n_] := A006822[[n + 1]] - A058276[[n + 1]];
%t A184963 a /@ Range[0, 17] (* _Jean-François Alcover_, Jan 27 2020 *)
%Y A184963 Connected 6-regular simple graphs with girth at least g: A006822 (g=3), A058276 (g=4).
%Y A184963 Connected 6-regular simple graphs with girth exactly g: this sequence (g=3), A184964 (g=4).
%K A184963 nonn,hard,more
%O A184963 0,10
%A A184963 _Jason Kimberley_, Feb 28 2011