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A185130 Irregular triangle E(n,g) counting not necessarily connected 3-regular simple graphs on 2n vertices with girth exactly g.

%I A185130 #15 Jan 06 2013 11:00:53
%S A185130 1,1,1,4,2,15,5,1,71,21,2,428,103,8,1,3406,752,48,1,34270,7385,450,5,
%T A185130 418621,91939,5752,32,5937051,1345933,90555,385,94782437,22170664,
%U A185130 1612917,7573,1,1670327647,401399440,31297424,181224,3,32090011476,7887389438
%N A185130 Irregular triangle E(n,g) counting not necessarily connected 3-regular simple graphs on 2n vertices with girth exactly g.
%C A185130 The first column is for girth exactly 3. The column for girth exactly g begins when 2n reaches A000066(g).
%H A185130 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 A185130 The n-th row is the sequence of differences of the n-th row of A185330:
%F A185130 E(n,g) = A185330(n,g) - A185330(n,g+1), once we have appended 0 to each row of A185330.
%F A185130 Hence the sum of the n-th row is A185330(n,3) = A005638(n).
%e A185130 1;
%e A185130 1, 1;
%e A185130 4, 2;
%e A185130 15, 5, 1;
%e A185130 71, 21, 2;
%e A185130 428, 103, 8, 1;
%e A185130 3406, 752, 48, 1;
%e A185130 34270, 7385, 450, 5;
%e A185130 418621, 91939, 5752, 32;
%e A185130 5937051, 1345933, 90555, 385;
%e A185130 94782437, 22170664, 1612917, 7573, 1;
%e A185130 1670327647, 401399440, 31297424, 181224, 3;
%e A185130 32090011476, 7887389438, 652159986, 4624481, 21;
%e A185130 666351752261, 166897766824, 14499787794, 122089999, 545, 1;
%e A185130 14859579573845, 3781593764772, 342646826428, 3328899592, 30368, 0;
%Y A185130 Initial columns of this triangle: A185133 (g=3), A185134 (g=4), A185135 (g=5), A185136 (g=6).
%K A185130 nonn,hard,tabf
%O A185130 2,4
%A A185130 _Jason Kimberley_, Dec 26 2012