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.

Previous Showing 11-19 of 19 results.

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

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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).

A185203 Number of disconnected 10-regular graphs with n nodes.

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, 1, 1, 11, 550, 806174, 2585947720, 9802278927562, 42709859521915286, 214798119408798346811, 1251607430636395979871600, 8463468717232507491862780325, 66406919318277846825588474735084
Offset: 0

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Author

Jason Kimberley, Jan 26 2012

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10-regular simple graphs: A014382 (connected), this sequence (disconnected).
Disconnected regular simple graphs: A068932 (any degree), A068933 (triangular array), specified degree k: A165652 (k=2), A165653 (k=3), A033483 (k=4), A165655 (k=5), A165656 (k=6), A165877 (k=7), A165878 (k=8), A185293 (k=9), this sequence (k=10), A185213 (k=11).

Extensions

Terms a(29) and beyond from Andrew Howroyd, May 20 2020

A185213 Number of disconnected 11-regular graphs with 2n nodes.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 13, 8037887, 945095928322681, 187549741420313256356540, 66398446859255608487987488813721, 43100445877221052008718432480116589483823
Offset: 0

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Author

Jason Kimberley, Jan 26 2012

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11-regular simple graphs: A014384 (connected), this sequence (disconnected).
Disconnected regular simple graphs: A068932 (any degree), A068933 (triangular array), specified degree k: A165652 (k=2), A165653 (k=3), A033483 (k=4), A165655 (k=5), A165656 (k=6), A165877 (k=7), A165878 (k=8), A185293 (k=9), A185203 (k=10), this sequence (k=11).

Extensions

a(15)-a(18) from Andrew Howroyd, May 20 2020

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

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Author

Jason Kimberley, Oct 27 2012

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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).

A185293 Number of disconnected 9-regular graphs with 2n nodes.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 9, 88238, 113315027550, 281342192047999912, 1251394783006077652496450, 9854615127100313024544239975139, 134283364935428822131144679491097123786
Offset: 0

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Author

Jason Kimberley, Jan 26 2012

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9-regular simple graphs: A014381 (connected), this sequence (disconnected).
Disconnected regular simple graphs: A068932 (any degree), A068933 (triangular array), specified degree k: A157928 (k=0), A157928 (k=1), A165652 (k=2), A165653 (k=3), A033483 (k=4), A165655 (k=5), A165656 (k=6), A165877 (k=7), A165878 (k=8), this sequence (k=9), A185203 (k=10), A185213 (k=11).

Extensions

a(14)-a(17) from Andrew Howroyd, May 20 2020

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

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Author

Jason Kimberley, Apr 02 2012

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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).

Formula

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

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Author

Jason Kimberley, Dec 14 2012

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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

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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).

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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).

A054916 Number of connected unlabeled regular graphs with n nodes such that complement is also connected.

Original entry on oeis.org

1, 0, 0, 0, 1, 2, 2, 12, 18, 158, 532, 18956, 389418, 50314722, 2942198334, 1698517035792, 442786966113484, 649978211591577760, 429712868499646362046, 2886054228478618206288948, 8835589045148342277740379344, 152929279364927228928017067050204, 1207932509391069805495173186013097090, 99162609848561525198669168626676490270856
Offset: 1

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Author

N. J. A. Sloane, May 23 2000

Keywords

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Crossrefs

Cf. A005176, A005177, A068932.

Formula

a(n) = 2*A005177(n)-A005176(n) = A005177(n)-A068932(n).

Extensions

Terms a(11)-a(16) appended, journal link changed to article link, and second formula included, by Jason Kimberley, Oct 24 2009
a(17)-a(24) from Andrew Howroyd, May 19 2020
Previous Showing 11-19 of 19 results.

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