%I #9 Jan 06 2013 14:32:39

%S 1,1,2,5,1,16,0,58,2,264,2,1535,12,10755,31,87973,220,803973,1606,

%T 8020967,16829,86029760,193900,983431053,2452820,11913921910,32670331,

%U 1,152352965278,456028487,2,2050065073002,6636066126,8,28466234288520,100135577863,131,8020967,16829

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

%C The first column is for girth at least 3. The column for girth g commences when n reaches A037233(g).

%H 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 The n-th row is the sequence of differences of the n-th row of A185340:

%F E(n,g) = A185340(n,g) - A185340(n,g+1), once we have appended 0 to each row of A185340.

%F Hence the sum of the n-th row is A185340(n,3) = A033301(n).

%e 05: 1;

%e 06: 1;

%e 07: 2;

%e 08: 5, 1;

%e 09: 16, 0;

%e 10: 58, 2;

%e 11: 264, 2;

%e 12: 1535, 12;

%e 13: 10755, 31;

%e 14: 87973, 220;

%e 15: 803973, 1606;

%e 16: 8020967, 16829;

%e 17: 86029760, 193900;

%e 18: 983431053, 2452820;

%e 19: 11913921910, 32670331, 1;

%e 20: 152352965278, 456028487, 2;

%e 21: 2050065073002, 6636066126, 8;

%e 22: 28466234288520, 100135577863, 131;

%Y Initial columns of this triangle: A185143 (g=3), A185144 (g=4).

%K nonn,hard,tabf

%O 5,3

%A _Jason Kimberley_, Jan 06 2013