A185214 -id:A185214 - cp's OEIS frontend

A185284 Number of disconnected 8-regular simple graphs on n vertices with girth at least 4.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 14, 1

Offset: 0

Jason Kimberley, Feb 22 2011

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g

Disconnected k-regular simple graphs with girth at least 4: A185214 (any k), A185204 (triangle); specified degree k: A185224 (k=2), A185234 (k=3), A185244 (k=4), A185254 (k=5), A185264 (k=6), A185274 (k=7), this sequence (k=8), A185294 (k=9).

A185294 Number of disconnected 9-regular simple graphs on 2n vertices with girth at least 4.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 15

Offset: 0

Jason Kimberley, Feb 22 2011

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g

Disconnected k-regular simple graphs with girth at least 4: A185214 (any k), A185204 (triangle); specified degree k: A185224 (k=2), A185234 (k=3), A185244 (k=4), A185254 (k=5), A185264 (k=6), A185274 (k=7), A185284 (k=8), this sequence (k=9).

A185217 Number of disconnected regular simple graphs on n vertices with girth at least 7.

Original entry on oeis.org

0, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 4, 3, 5, 4, 6, 6, 8, 8, 11, 11, 14, 15, 19, 20, 25, 27, 33, 36, 43, 48, 57, 63, 74, 83, 97, 108, 126, 141, 163, 183, 210, 236, 272, 304, 350, 390, 471, 498, 1175, 635, 32957, 807, 1886322, 1022, 101215816, 1291, 5025322391

Offset: 0

Jason Kimberley, Oct 27 2012

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g

Disconnected regular graphs with girth at least g: A068932 (g=3), A185214 (g=4), A185215 (g=5), A185216 (g=6), this sequence (g=7).

Disconnected k-regular simple graphs with girth at least 7: this sequence (all k), A185207 (triangle); A185227 (k=2), A185237 (k=3).

A210713 Number of disconnected regular simple graphs on n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 5, 4, 16, 13, 64, 98, 597, 2064, 22472, 112814, 4799607, 31138903, 4207941575, 115979716284, 13482672620149

Offset: 0

Jason Kimberley, Apr 02 2012

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

This sequence is the row sum sequence of the triangle A210703.

Disconnected k-regular simple graphs with girth exactly 3: this sequence (any k), A210703 (triangle); for fixed k: A185033 (k=3), A185043 (k=4), A185053 (k=5), A185063 (k=6).

a(n) = A068932(n) - A185214(n).

A185218 Number of disconnected regular simple graphs on n vertices with girth at least 8.

Original entry on oeis.org

0, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 8, 7, 10, 10, 13, 13, 17, 17, 22, 23, 28, 30, 37, 39, 47, 51, 61, 66, 78, 85, 100, 110, 127, 140, 163, 179, 206, 228, 261, 289, 330, 365, 416, 461, 522, 579, 657, 726, 819, 909, 1024, 1134, 1277, 1411

Offset: 0

Jason Kimberley, Dec 14 2012

Jason Kimberley, Table of n, a(n) for n = 0..77
Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g

Disconnected regular graphs with girth at least g: A068932 (g=3), A185214 (g=4), A185215 (g=5), A185216 (g=6), A185217 (g=7), this sequence (g=8).

A185219 Number of disconnected regular simple graphs on n vertices with girth at least 9.

Original entry on oeis.org

0, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 7, 9, 9, 12, 12, 15, 16, 19, 20, 25, 26, 31, 34, 40, 43, 51, 55, 64, 71, 81, 89, 103, 113, 129, 143, 162, 179, 204, 225, 254, 282, 317, 351, 396, 437, 490, 544, 608, 673, 753, 832, 928, 1028, 1144, 1264

Offset: 0

Jason Kimberley, Dec 19 2012

			a(116) = 89574 because there is 1 such 0-regular graph (116 disconnected vertices), 1 such 1-regular graph (58 loose edges), A185229(116) = 89401, and 171 such 3-regular graphs (because A210709(58)=18).

Jason Kimberley, Table of n, a(n) for n = 0..116
Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g

Disconnected regular graphs with girth at least g: A068932 (g=3), A185214 (g=4), A185215 (g=5), A185216 (g=6), A185217 (g=7), A185218 (g=8), this sequence (g=9).

A210714 Number of disconnected regular simple graphs on n vertices with girth exactly 4.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3, 2, 5, 3, 15, 5, 44, 10, 203, 47, 1415, 1710, 27771, 197951, 2613710, 33117920, 463707092, 6709514282, 102306345333, 1597440872721

Offset: 0

Jason Kimberley, Dec 10 2012

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {, }][[All, 2]]];
A185214 = A@185214;
A185215 = A@185215;
a[n_] := A185214[[n + 1]] - A185215[[n + 1]];
a /@ Range[0, 31] (* Jean-François Alcover, Jan 27 2020 *)

a(n) = A185214(n) - A185215(n).

a(31) corrected by the author, propagated from A185244, Jan 05 2013

cp's OEIS Frontend

A185284 Number of disconnected 8-regular simple graphs on n vertices with girth at least 4.

Views

Author

Keywords

Links

Crossrefs

A185294 Number of disconnected 9-regular simple graphs on 2n vertices with girth at least 4.

Views

Author

Keywords

Links

Crossrefs

A185217 Number of disconnected regular simple graphs on n vertices with girth at least 7.

Views

Author

Keywords

Links

Crossrefs

A210713 Number of disconnected regular simple graphs on n vertices with girth exactly 3.

Views

Author

Keywords

Links

Crossrefs

Formula

A185218 Number of disconnected regular simple graphs on n vertices with girth at least 8.

Views

Author

Keywords

Links

Crossrefs

A185219 Number of disconnected regular simple graphs on n vertices with girth at least 9.

Views

Author

Keywords

Examples

Links

Crossrefs

A210714 Number of disconnected regular simple graphs on n vertices with girth exactly 4.

Views

Author

Keywords

Links

Programs

Mathematica

Formula

Extensions