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A185140 Irregular triangle E(n,g) counting not necessarily connected 4-regular simple graphs on n vertices with girth exactly g.

%I A185140 #9 Jan 06 2013 14:32:39
%S A185140 1,1,2,5,1,16,0,58,2,264,2,1535,12,10755,31,87973,220,803973,1606,
%T A185140 8020967,16829,86029760,193900,983431053,2452820,11913921910,32670331,
%U A185140 1,152352965278,456028487,2,2050065073002,6636066126,8,28466234288520,100135577863,131,8020967,16829
%N A185140 Irregular triangle E(n,g) counting not necessarily connected 4-regular simple graphs on n vertices with girth exactly g.
%C A185140 The first column is for girth at least 3. The column for girth g commences when n reaches A037233(g).
%H A185140 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 A185140 The n-th row is the sequence of differences of the n-th row of A185340:
%F A185140 E(n,g) = A185340(n,g) - A185340(n,g+1), once we have appended 0 to each row of A185340.
%F A185140 Hence the sum of the n-th row is A185340(n,3) = A033301(n).
%e A185140 05: 1;
%e A185140 06: 1;
%e A185140 07: 2;
%e A185140 08: 5, 1;
%e A185140 09: 16, 0;
%e A185140 10: 58, 2;
%e A185140 11: 264, 2;
%e A185140 12: 1535, 12;
%e A185140 13: 10755, 31;
%e A185140 14: 87973, 220;
%e A185140 15: 803973, 1606;
%e A185140 16: 8020967, 16829;
%e A185140 17: 86029760, 193900;
%e A185140 18: 983431053, 2452820;
%e A185140 19: 11913921910, 32670331, 1;
%e A185140 20: 152352965278, 456028487, 2;
%e A185140 21: 2050065073002, 6636066126, 8;
%e A185140 22: 28466234288520, 100135577863, 131;
%Y A185140 Initial columns of this triangle: A185143 (g=3), A185144 (g=4).
%K A185140 nonn,hard,tabf
%O A185140 5,3
%A A185140 _Jason Kimberley_, Jan 06 2013