cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A185315 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 5.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 3, 2, 3, 2, 5, 3, 7, 4, 15, 6, 57, 8, 466, 12, 5801, 24, 91091, 3939, 1744378, 4132022, 163639295, 4018022192, 119026596500
Offset: 0

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Author

Jason Kimberley, Dec 12 2012

Keywords

Links

Crossrefs

Not necessarily connected k-regular simple graphs with girth at least 5: this sequence (any k), A185305 (triangle); specified degree k: A185325 (k=2), A185335 (k=3).
Not necessarily connected regular simple graphs with girth at least g: A005176 (g=3), A185314 (g=4), this sequence (g=5), A185316 (g=6), A185317 (g=7), A185318 (g=8), A185319 (g=9).

Formula

a(n) = A186725(n) + A185215(n).

A185216 Number of disconnected regular simple graphs on n vertices with girth at least 6.

Original entry on oeis.org

0, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 4, 3, 5, 4, 7, 6, 9, 9, 12, 12, 17, 17, 22, 24, 31, 32, 42, 44, 60, 60, 109, 80, 529, 107, 8246, 143, 191422, 188, 4856141, 248, 127938143, 326, 3482858640, 424, 98176518751, 552
Offset: 0

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Author

Jason Kimberley, Jun 21 2012

Keywords

Links

Crossrefs

Disconnected k-regular simple graphs with girth at least 6: this sequence (all k), A185206 (triangle); A185226 (k=2), A185236 (k=3), A185246 (k=4).
Disconnected regular graphs with girth at least g: A068932 (g=3), A185214 (g=4), A185215 (g=5), this sequence (g=6), A185217 (g=7).

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

Views

Author

Jason Kimberley, Oct 27 2012

Keywords

Links

Crossrefs

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).

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

Views

Author

Jason Kimberley, Dec 14 2012

Keywords

Links

Crossrefs

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

Views

Author

Jason Kimberley, Dec 19 2012

Keywords

Examples

			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).

Links

Crossrefs

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

Views

Author

Jason Kimberley, Dec 10 2012

Keywords

Links

Programs

  • Mathematica
    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 *)

Formula

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

Extensions

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

A210715 Number of disconnected regular simple graphs on n vertices with girth exactly 5.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 6, 6, 9, 9, 22, 13, 82, 18, 618, 26, 7164, 36, 107862, 50, 1876730, 70, 35924810, 95, 741405213, 131, 16356067216, 323, 383931367731, 132977
Offset: 0

Views

Author

Jason Kimberley, Dec 10 2012

Keywords

Links

Formula

a(n) = A185215(n) - A185216(n).
Showing 1-7 of 7 results.

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