A185244 -id:A185244 - cp's OEIS frontend

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

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).

A185344 Number of not necessarily connected 4-regular simple graphs on n vertices with girth at least 4.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 12, 31, 220, 1606, 16829, 193900, 2452820, 32670332, 456028489, 6636066134, 100135577994, 1582718914660

Offset: 0

Jason Kimberley, Nov 03 2011

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

4-regular simple graphs with girth at least 4: A033886 (connected), A185244 (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), this sequence (k=4), A185354 (k=5), A185364 (k=6).

A033886 = Cases[Import["https://oeis.org/A033886/b033886.txt", "Table"], {, }][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A033886] (* Jean-François Alcover, Dec 04 2019, updated Mar 18 2020 *)

This sequence is the Euler transformation of A033886.

a(n) = A033886(n) + A185244(n).

A185043 Number of disconnected 4-regular simple graphs on n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 8, 25, 88, 377, 2026, 13349, 104593, 930571, 9124627, 96699740, 1095467916, 13175254799, 167460501260, 2241576473025, 31510509517563, 464047467911837, 7143984462730072, 114749034352969037, 1919656978492976231

Offset: 0

Jason Kimberley, Feb 29 2012

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

4-regular simple graphs with girth exactly 3: A184943 (connected), this sequence (disconnected), A185143 (not necessarily connected).
Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), A210703 (triangle); for fixed k: A185033 (k=3), this sequence (k=4), A185053 (k=5), A185063 (k=6).
Disconnected 4-regular simple graphs with girth exactly g: this sequence (g=3), A185044 (g=4).

a(n) = A033483(n) - A185244(n).

Terms a(27)-a(31), due to the extension of A006820 by Andrew Howroyd, from Jason Kimberley, Mar 16 2020

A185246 Number of disconnected 4-regular simple graphs on n vertices with girth at least 6.

Original entry on oeis.org

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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 5, 0, 23, 0, 1301, 25, 495379, 13529

Offset: 0

Jason Kimberley, Feb 22 2011

Jason Kimberley, Disconnected regular graphs with girth at least 6
Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g

4-regular simple graphs with girth at least 4: A058348 (connected), this sequence (disconnected), A185346 (not necessarily connected).
Disconnected 4-regular simple graphs with girth at least g: A033483 (g=3), A185244 (g=4), A185245 (g=5), this sequence (g=6).
Disconnected k-regular simple graphs with girth at least 6: A185216 (all k), A185206 (triangle); A185226 (k=2), A185236 (k=3), this sequence (k=4).

a(n) = A185346(n) - A058348(n) = Euler_transformation(A058348)(n) - A058348(n).

A185044 Number of disconnected 4-regular simple graphs on n vertices with girth exactly 4.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 15, 35, 247, 1692, 17409, 197924, 2492824, 33117880, 461597957, 6709514218, 101153412903, 1597440868898

Offset: 0

Jason Kimberley, Nov 04 2011

Only one component need have girth exactly four; the other components need only have girth at least four.

First differs from A185244 at n = 38, the smallest n where A185245 is nonzero.

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

Disconnected 4-regular simple graphs with girth exactly g: A185043 (g=3), this sequence (g=4).

Disconnected k-regular simple graphs with girth exactly 4: A185034 (k=3), this sequence (k=4).

a(n) = A185244(n) - A185245(n).

a(n) = A185144(n) - A184944(n).

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

A185245 Number of disconnected 4-regular simple graphs on n vertices with girth at least 5.

Original entry on oeis.org

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, 0, 0, 0, 0, 0, 0, 1, 2, 11, 147, 4215, 132741, 4419691, 141928589, 4339298225, 128489587646

Offset: 0

Jason Kimberley, Feb 22 2011

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

Disconnected 4-regular simple graphs with girth at least g: A033483 (g=3), A185244 (g=4), this sequence (g=5), A185246 (g=6).

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

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

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A185344 Number of not necessarily connected 4-regular simple graphs on n vertices with girth at least 4.

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A185043 Number of disconnected 4-regular simple graphs on n vertices with girth exactly 3.

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A185246 Number of disconnected 4-regular simple graphs on n vertices with girth at least 6.

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A185044 Number of disconnected 4-regular simple graphs on n vertices with girth exactly 4.

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A185245 Number of disconnected 4-regular simple graphs on n vertices with girth at least 5.

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

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Author

Keywords

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Programs

Mathematica

Formula

Extensions