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A185643 Triangular array E(n,k) counting, not necessarily connected, k-regular simple graphs on n vertices with girth exactly 3.

%I A185643 #18 Feb 08 2013 17:35:00
%S A185643 0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,1,1,1,0,0,1,0,2,0,1,0,0,1,4,5,3,
%T A185643 1,1,0,0,2,0,16,0,4,0,1,0,0,2,15,58,59,21,5,1,1,0,0,3,0,264,0,266,0,6,
%U A185643 0,1,0,0,4,71,1535,7848,7848,1547,94,9,1,1,0,0,5,0,10755,0,367860,0,10786,0,10,0,1
%N A185643 Triangular array E(n,k) counting, not necessarily connected, k-regular simple graphs on n vertices with girth exactly 3.
%H A185643 Jason Kimberley, <a href="/A185643/b185643.txt">Table of i, a(i)=E(n,k) for i = 1..136 (n = 1..16)</a>
%H A185643 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/E_k-reg_girth_eq_g_index">Index of sequences counting not necessarily connected k-regular simple graphs with girth exactly g</a>
%F A185643 E(n,k) = A186733(n,k) + A210703(n,k), noting that A210703 is a tabf.
%F A185643 E(n,k) = A051031(n,k) - A185304(n,k), noting that A185304 is a tabf.
%e A185643 01: 0;
%e A185643 02: 0, 0;
%e A185643 03: 0, 0, 1;
%e A185643 04: 0, 0, 0, 1;
%e A185643 05: 0, 0, 0, 0, 1;
%e A185643 06: 0, 0, 1, 1, 1, 1;
%e A185643 07: 0, 0, 1, 0, 2, 0, 1;
%e A185643 08: 0, 0, 1, 4, 5, 3, 1, 1;
%e A185643 09: 0, 0, 2, 0, 16, 0, 4, 0, 1;
%e A185643 10: 0, 0, 2, 15, 58, 59, 21, 5, 1, 1;
%e A185643 11: 0, 0, 3, 0, 264, 0, 266, 0, 6, 0, 1;
%e A185643 12: 0, 0, 4, 71, 1535, 7848, 7848, 1547, 94, 9, 1, 1;
%e A185643 13: 0, 0, 5, 0, 10755, 0, 367860, 0, 10786, 0, 10, 0, 1;
%e A185643 14: 0, 0, 6, 428, 87973, 3459379, 21609300, 21609300, 3459386, 88193, 540, 13, 1, 1;
%e A185643 15: 0, 0, 9, 0, 803973, 0, 1470293675, 0, 1470293676, 0, 805579, 0, 17, 0, 1;
%e A185643 16: 0, 0, 10, 3406, 8020967, 2585136353, 113314233804, 733351105934, 733351105934, 113314233813, 2585136741, 8037796, 4207, 21, 1, 1;
%Y A185643 The sum of the n-th row of this sequence is A198313(n).
%Y A185643 Not necessarily connected k-regular simple graphs girth exactly 3: A198313 (any k), this sequence (triangle); fixed k: A026796 (k=2), A185133 (k=3), A185143 (k=4), A185153 (k=5), A185163 (k=6).
%K A185643 nonn,hard,tabl
%O A185643 1,26
%A A185643 _Jason Kimberley_, Feb 07 2013