cp's OEIS Frontend

A185305 Triangular array E(n,k) counting not necessarily connected k-regular simple graphs on n vertices with girth at least 5.

%I A185305 #8 Feb 20 2013 17:44:10
%S A185305 1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,2,1,1,0,2,0,1,1,3,2,
%T A185305 1,0,3,0,1,1,4,9,1,0,5,0,1,1,6,49,1,0,7,0,1,1,9,455,1,0,10,0,1,1,1,13,
%U A185305 5784,2,1,0,15,0,8,1,1,18,90940,131,1,0,21,0,3917,1,1,26,1620491,123859
%N A185305 Triangular array E(n,k) counting not necessarily connected k-regular simple graphs on n vertices with girth at least 5.
%C A185305 Row sums give A185315.
%H A185305 Jason Kimberley, <a href="/A185305/b185305.txt">Table of n, a(i)=E(n,k) for i = 1..108 (n = 1..28)</a>
%H A185305 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/E_girth_ge_5">Not necessarily connected k-regular graphs with girth at least 5</a>
%H A185305 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/E_k-reg_girth_ge_g_index">Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g</a>
%F A185305 E(n,k) = A186715(n,k) + A185205(n,k).
%e A185305 01: 1;
%e A185305 02: 1, 1;
%e A185305 03: 1, 0;
%e A185305 04: 1, 1;
%e A185305 05: 1, 0, 1;
%e A185305 06: 1, 1, 1;
%e A185305 07: 1, 0, 1;
%e A185305 08: 1, 1, 1;
%e A185305 09: 1, 0, 1;
%e A185305 10: 1, 1, 2, 1;
%e A185305 11: 1, 0, 2, 0;
%e A185305 12: 1, 1, 3, 2;
%e A185305 13: 1, 0, 3, 0;
%e A185305 14: 1, 1, 4, 9;
%e A185305 15: 1, 0, 5, 0;
%e A185305 16: 1, 1, 6, 49;
%e A185305 17: 1, 0, 7, 0;
%e A185305 18: 1, 1, 9, 455;
%e A185305 19: 1, 0, 10, 0, 1;
%e A185305 20: 1, 1, 13, 5784, 2;
%e A185305 21: 1, 0, 15, 0, 8;
%e A185305 22: 1, 1, 18, 90940, 131;
%e A185305 23: 1, 0, 21, 0, 3917;
%e A185305 24: 1, 1, 26, 1620491, 123859;
%e A185305 25: 1, 0, 30, 0, 4131991;
%e A185305 26: 1, 1, 36, 31478649, 132160608;
%e A185305 27: 1, 0, 42, 0, 4018022149;
%e A185305 28: 1, 1, 50, 656784488, 118369811960;
%Y A185305 Not necessarily connected k-regular simple graphs with girth at least 5: A185315 (any k), this sequence (triangle); specified degree k: A185325 (k=2), A185335 (k=3).
%K A185305 nonn,hard,tabf
%O A185305 1,25
%A A185305 _Jason Kimberley_, Feb 21 2013