A185364
Not necessarily connected 6-regular simple graphs on n vertices with girth at least 4.
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 9, 6, 267, 3727, 483012, 69823723, 14836130862
Offset: 0
6-regular simple graphs with girth at least 4:
A058276 (connected),
A185264 (disconnected), this sequence (not necessarily connected).
Not necessarily connected k-regular simple graphs with girth at least 4:
A185314 (any k),
A185304 (triangle); specified degree k:
A008484 (k=2),
A185334 (k=3),
A185344 (k=4),
A185354 (k=5), this sequence (k=6).
A185336
Number of not necessarily connected 3-regular simple graphs on 2n vertices with girth at least 6.
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 0, 1, 1, 5, 32, 385, 7574, 181227, 4624502, 122090545, 3328929960, 93990692632, 2754222605808
Offset: 0
3-regular simple graphs with girth at least 6:
A014374 (connected),
A185236 (disconnected), this sequence (not necessarily connected).
Not necessarily connected k-regular simple graphs with girth at least 6:
A185326 (k=2), this sequence (k=3).
Not necessarily connected 3-regular simple graphs with girth *at least* g:
A005638 (g=3),
A185334 (g=4),
A185335 (g=5), this sequence (g=6).
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A014374 = Cases[Import["https://oeis.org/A014374/b014374.txt", "Table"], {, }][[All, 2]];
etr[f_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d f[d], {d, Divisors[j]}] b[n - j], {j, 1, n}]/n]; b];
a = etr[A014374[[# + 1]]&];
a /@ Range[0, Length[A014374] - 1] (* Jean-François Alcover, Dec 04 2019 *)
A185330
Irregular triangle E(n,g) counting not necessarily connected 3-regular simple graphs on 2n vertices with girth at least g.
Original entry on oeis.org
1, 2, 1, 6, 2, 21, 6, 1, 94, 23, 2, 540, 112, 9, 1, 4207, 801, 49, 1, 42110, 7840, 455, 5, 516344, 97723, 5784, 32, 7373924, 1436873, 90940, 385, 118573592, 23791155, 1620491, 7574, 1, 2103205738, 432878091, 31478651, 181227, 3, 40634185402
Offset: 2
1;
2, 1;
6, 2;
21, 6, 1;
94, 23, 2;
540, 112, 9, 1;
4207, 801, 49, 1;
42110, 7840, 455, 5;
516344, 97723, 5784, 32;
7373924, 1436873, 90940, 385;
118573592, 23791155, 1620491, 7574, 1;
2103205738, 432878091, 31478651, 181227, 3;
40634185402, 8544173926, 656784488, 4624502, 21;
847871397424, 181519645163, 14621878339, 122090545, 546, 1;
18987149095005, 4127569521160, 345975756388, 3328929960, 30368, 0;
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