A054581 -id:A054581 - cp's OEIS frontend

A078792 Number of unlabeled 3-trees on n vertices.

0, 0, 1, 1, 1, 2, 5, 15, 58, 275, 1505, 9003, 56931, 372973, 2506312, 17165954, 119398333, 841244274, 5993093551, 43109340222, 312747109787, 2286190318744, 16826338257708, 124605344758149, 927910207739261, 6945172081954449, 52225283886702922

Offset: 1

Gordon F. Royle, Dec 05 2002

nonn

A k-tree is recursively defined as follows: K_k is a k-tree and any k-tree on n+1 vertices is obtained by joining a new vertex to a k-clique in a k-tree on n vertices.

Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 328.

Allan Bickle, A Survey of Maximal k-degenerate Graphs and k-Trees, Theory and Applications of Graphs 0 1 (2024) Article 5.
Andrew Gainer-Dewar, Gamma-Species and the Enumeration of k-Trees, Electronic Journal of Combinatorics, Volume 19 (2012), #P45. - From _N. J. A. Sloane_, Dec 15 2012
Eric Weisstein's World of Mathematics, k-Tree.

Column k=3 of A370770.

Cf. A036362 (labeled 3-trees), A054581 (unlabeled 2-trees).

More terms from Andrew R. Gainer, Dec 03 2011

A063687 Number of 2-trees rooted at any symmetric edge.

Original entry on oeis.org

1, 1, 1, 2, 3, 6, 10, 21, 38, 84, 156, 352, 677, 1562, 3054, 7148, 14196, 33603, 67474, 161121, 326519, 785305, 1603111, 3878194, 7965845, 19365811, 39983300, 97610247, 202424674, 495955345, 1032460679, 2537529717, 5300256499

Offset: 0

Vladeta Jovovic, Aug 22 2001

nonn

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 75, Eq. (3.5.9).

Cf. A058870, A058866, A054581.

A201702 Number of unlabeled 5-trees on n nodes.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 1, 2, 5, 15, 64, 342, 2321, 18578, 168287, 1656209, 17288336, 188006362, 2105867058, 24108331027, 280638347609, 3310098377912, 39462525169310, 474697793413215, 5754095507495584, 70216415130786725, 861924378411516159, 10636562125193377459

Offset: 1

Andrew R. Gainer, Dec 03 2011

nonn

A k-tree is recursively defined as follows: K_k is a k-tree and any k-tree on n+1 vertices is obtained by joining a vertex to a k-clique in a k-tree on n vertices.

Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 328.

Allan Bickle, A Survey of Maximal k-degenerate Graphs and k-Trees, Theory and Applications of Graphs 0 1 (2024) Article 5.
Andrew Gainer-Dewar, Gamma-Species and the Enumeration of k-Trees, Electronic Journal of Combinatorics, Volume 19 (2012), #P45. - From _N. J. A. Sloane_, Dec 15 2012
Eric Weisstein's World of Mathematics, k-Tree

Column k=5 of A370770.

Cf. A054581 (unlabeled 2-trees), A078792 (unlabeled 3-trees), A078793 (unlabeled 4-trees).

A202037 Number of unlabeled 6-trees on n nodes.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 1, 2, 5, 15, 64, 342, 2344, 19090, 179562, 1878277, 21365403, 258965451, 3294561195, 43472906719, 589744428065, 8171396893523, 115094557122380, 1642269376265063, 23679803216530017, 344396036645439675, 5045351124912000756

Offset: 1

Andrew R. Gainer, Dec 09 2011

nonn

A k-tree is recursively defined as follows: K_k is a k-tree and any k-tree on n+1 vertices is obtained by joining a vertex to a k-clique in a k-tree on n vertices.

Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 328.

Allan Bickle, A Survey of Maximal k-degenerate Graphs and k-Trees, Theory and Applications of Graphs 0 1 (2024) Article 5.
Andrew Gainer-Dewar, Gamma-Species and the Enumeration of k-Trees, Electronic Journal of Combinatorics, Volume 19 (2012), #P45. - From _N. J. A. Sloane_, Dec 15 2012

Column k=6 of A370770.

Cf. A054581 (unlabeled 2-trees), A078792 (unlabeled 3-trees), A078793 (unlabeled 4-trees), A201702 (unlabeled 5-trees)

A094610 Number of unlabeled 4-gonal 2-trees with n 4-gons.

Original entry on oeis.org

1, 1, 1, 3, 8, 32, 141, 749, 4304, 26492, 169263, 1115015, 7507211, 51466500, 358100288, 2523472751, 17978488711, 129325796854, 938234533024, 6858551493579, 50478955083341, 373815860588360, 2783730088637429, 20835514668765200, 156675846789962554, 1183195305751233833

Offset: 0

Vladeta Jovovic, Jun 06 2004

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..500
G. Labelle, C. Lamathe and P. Leroux, Labeled and unlabeled enumeration of k-gonal 2-trees

Column k=4 of A340811.

Cf. A054581.

Terms a(21) and beyond from Andrew Howroyd, May 09 2021

A094611 Number of unlabeled pentagonal 2-trees with n pentagons.

Original entry on oeis.org

1, 1, 1, 3, 11, 56, 359, 2597, 20386, 167819, 1429815, 12500748, 111595289, 1013544057, 9340950309, 87176935700, 822559721606, 7836316493485, 75293711520236, 728968295958626, 7105984356424859, 69697524828651997, 687448151462822966, 6815174949649428254

Offset: 0

Vladeta Jovovic, Jun 06 2004

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..200
G. Labelle, C. Lamathe and P. Leroux, Labeled and unlabeled enumeration of k-gonal 2-trees

Column k=5 of A340811.

Cf. A054581.

Terms a(21) and beyond from Andrew Howroyd, May 09 2021

A094637 Number of unlabeled hexagonal 2-trees with n hexagons.

Original entry on oeis.org

1, 1, 1, 4, 16, 103, 799, 7286, 71094, 729974, 7743818, 84307887, 937002302, 10595117272, 121568251909, 1412555701804, 16594126114458, 196829590326284, 2354703777373055, 28385225424840078, 344524656398655124, 4207569734885041198, 51674558137433627724

Offset: 0

Vladeta Jovovic, Jun 06 2004

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..200
G. Labelle, C. Lamathe and P. Leroux, Labeled and unlabeled enumeration of k-gonal 2-trees, arXiv:math/0312424 [math.CO], Dec 23 2003.

Column k=6 of A340811.

Cf. A054581.

Terms a(21) and beyond from Andrew Howroyd, Feb 02 2021

A094651 Number of unlabeled heptagonal 2-trees with n heptagons.

Original entry on oeis.org

1, 1, 1, 4, 20, 158, 1539, 16970, 199879, 2460350, 31266165, 407461893, 5420228329, 73352481577, 1007312969202, 14008437540003, 196963172193733, 2796235114720116, 40038505601111596, 577693117173844307, 8392528734991449808, 122680472402091278920, 1803416089912665770579

Offset: 0

Vladeta Jovovic, Jun 06 2004

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..200
G. Labelle, C. Lamathe and P. Leroux, Labeled and unlabeled enumeration of k-gonal 2-trees, arXiv:math/0312424 [math.CO], Dec 23 2003.

Column k=7 of A340811.

Cf. A054581.

Terms a(20) and beyond from Andrew Howroyd, Feb 02 2021

A094652 Number of unlabeled octagonal 2-trees with n octagons.

Original entry on oeis.org

1, 1, 1, 5, 26, 245, 2737, 35291, 483819, 6937913, 102666626, 1558022255, 24133790815, 380320794122, 6081804068869, 98490990290897, 1612634990857755, 26660840123167203, 444560998431678554, 7469779489114328514, 126375763235359105446, 2151342943131421629636

Offset: 0

Vladeta Jovovic, Jun 06 2004

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..200
G. Labelle, C. Lamathe and P. Leroux, Labeled and unlabeled enumeration of k-gonal 2-trees, arXiv:math/0312424 [math.CO], Dec 23 2003.

Column k=8 of A340811.

Cf. A054581.

Terms a(20) and beyond from Andrew Howroyd, Feb 02 2021

A094653 Number of unlabeled 9-gonal 2-trees with n 9-gons.

Original entry on oeis.org

1, 1, 1, 5, 32, 343, 4505, 66603, 1045335, 17115162, 289107854, 5007144433, 88516438360, 1591949961503, 29053438148676, 536972307386326, 10034276171127780, 189331187319203010, 3603141751525175854, 69097496637591215442, 1334213677527481808220, 25922717218623692348237

Offset: 0

Vladeta Jovovic, Jun 06 2004

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..200
G. Labelle, C. Lamathe and P. Leroux, Labeled and unlabeled enumeration of k-gonal 2-trees, arXiv:math/0312424 [math.CO], Dec 23 2003.

Column k=9 of A340811.

Cf. A054581.

Terms a(19) and beyond from Andrew Howroyd, Feb 02 2021

cp's OEIS Frontend

A078792 Number of unlabeled 3-trees on n vertices.

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A063687 Number of 2-trees rooted at any symmetric edge.

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A201702 Number of unlabeled 5-trees on n nodes.

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A202037 Number of unlabeled 6-trees on n nodes.

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A094610 Number of unlabeled 4-gonal 2-trees with n 4-gons.

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A094611 Number of unlabeled pentagonal 2-trees with n pentagons.

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A094637 Number of unlabeled hexagonal 2-trees with n hexagons.

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A094651 Number of unlabeled heptagonal 2-trees with n heptagons.

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A094652 Number of unlabeled octagonal 2-trees with n octagons.

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A094653 Number of unlabeled 9-gonal 2-trees with n 9-gons.

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