A185314 -id:A185314 - cp's OEIS frontend

A185364 Not necessarily connected 6-regular simple graphs on n vertices with girth at least 4.

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

Jason Kimberley, Dec 07 2011

First differs from A058276 at n=24.

Jason Kimberley, Not necessarily connected k-regular graphs with girth at least 4
Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g

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).
Cf. A184964.

A058276 = Cases[Import["https://oeis.org/A058276/b058276.txt", "Table"], {, }][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A058276] (* Jean-François Alcover, Dec 04 2019, updated Mar 18 2020 *)

This sequence is the Euler transformation of A058276.

a(n) = A058276(n) + A185264(n).

A198314 Number of, not necessarily connected, regular simple graphs on n vertices with girth exactly 4.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 1, 0, 4, 1, 8, 3, 37, 33, 335, 1610, 17985, 193911, 2867313, 32674066, 1581626531, 6705889862

Offset: 0

Jason Kimberley, Dec 12 2012

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth exactly g

Not necessarily connected k-regular simple graphs girth exactly 4: this sequence (any k), A185644 (triangle); fixed k: A026797 (k=2), A185134 (k=3), A185144 (k=4).

Not necessarily connected regular simple graphs girth exactly g: A198313 (g=3), this sequence (g=4), A198315 (g=5), A198316 (g=6), A198317 (g=7), A198318 (g=8).

a(n) = A186744(n) + A210714(n).

a(n) = A185314(n) - A185315(n).

a(10) corrected from 9 to 8 by Jason Kimberley, Feb 22 2013

A185316 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 6.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 3, 2, 3, 2, 3, 2, 4, 3, 6, 4, 7, 5, 13, 7, 42, 10, 398, 13, 7592, 18, 181251, 25, 4624534, 33, 122090591, 45, 3328930034, 61, 93990693977, 106

Offset: 0

Jason Kimberley, Dec 12 2012

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g

Not necessarily connected regular simple graphs with girth at least g: A005176 (g=3), A185314 (g=4), A185315 (g=5), this sequence (g=6), A185317 (g=7), A185318 (g=8), A185319 (g=9).

a(n) = A186726(n) + A185216(n).

A185317 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 7.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 2, 2, 3, 2, 3, 2, 3, 2, 4, 3, 5, 4, 6, 5, 7, 7, 9, 9, 13, 12, 18, 16, 41, 21, 572, 28, 30402, 37, 1782884, 49, 95079141, 64, 4686063195, 84

Offset: 0

Jason Kimberley, Dec 12 2012

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g

Not necessarily connected regular simple graphs with girth at least g: A005176 (g=3), A185314 (g=4), A185315 (g=5), A185316 (g=6), this sequence (g=7), A185318 (g=8), A185319 (g=9).

a(n) = A186727(n) + A185217(n).

A185318 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 8.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 2, 1, 3, 2, 3, 2, 3, 2, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 9, 8, 11, 11, 14, 14, 19, 18, 23, 24, 30, 31, 41, 40, 61, 52, 217, 67, 4416, 86, 266463, 111, 20807816, 141

Offset: 0

Jason Kimberley, Dec 18 2012

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g

Not necessarily connected regular simple graphs with girth at least g: A005176 (g=3), A185314 (g=4), A185315 (g=5), A185316 (g=6), A185317 (g=7), this sequence (g=8), A185319 (g=9).

a(n) = A186728(n) + A185218(n).

A185319 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 9.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 8, 10, 10, 13, 13, 16, 17, 20, 21, 26, 27, 32, 35, 41, 44, 52, 56, 65, 72, 82, 90, 104, 114, 130, 144, 163, 180, 205, 226, 255, 283, 336

Offset: 0

Jason Kimberley, Dec 19 2012

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g

Not necessarily connected regular simple graphs with girth at least g: A005176 (g=3), A185314 (g=4), A185315 (g=5), A185316 (g=6), A185317 (g=7), A185318 (g=8), this sequence (g=9).

a(n) = A186729(n) + A185219(n).

cp's OEIS Frontend

A185364 Not necessarily connected 6-regular simple graphs on n vertices with girth at least 4.

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A198314 Number of, not necessarily connected, regular simple graphs on n vertices with girth exactly 4.

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A185316 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 6.

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A185317 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 7.

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A185318 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 8.

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A185319 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 9.

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