Nico Van Cleemput - cp's OEIS frontend

A243394 Number of isomorphism classes of connected 3-regular multigraphs with n vertices and with loops and semi-edges allowed.

2, 5, 7, 22, 43, 141, 373, 1270, 4053, 14671, 52826, 203289, 795581, 3241367, 13504130, 57904671, 253856990, 1139231977, 5219113084, 24401837085, 116278408069, 564380686932, 2787884851040, 14007277302822, 71538337097031, 371197207327709, 1955833646495247, 10459788214042492

Offset: 1

Nico Van Cleemput, Jun 04 2014

nonn

a(n) is also the number of isomorphism classes of connected multigraphs with n vertices of degree 3 or less and with loops allowed. - Andrew Howroyd, Mar 21 2020

G. Brinkmann, N. Van Cleemput, T. Pisanski, Generation of various classes of trivalent graphs, Theoretical Computer Science 502, 2013, pp.16-29.

Cf. A000421, A005967, A243391, A243392, A243393, A243394.

a(23)-a(28) from Andrew Howroyd, Mar 21 2020

A243393 Number of isomorphism classes of connected 3-regular loopless simple graphs with n vertices and with semi-edges allowed.

Original entry on oeis.org

1, 1, 2, 6, 10, 29, 64, 194, 531, 1733, 5524, 19430, 69322, 262044, 1016740, 4101318, 16996157, 72556640, 317558689, 1424644848, 6536588420, 30647561117, 146647344812, 715511358833, 3556531372395, 17996244725780, 92634418530686, 484756161038264

Offset: 1

Nico Van Cleemput, Jun 04 2014

nonn

Also: number of isomorphism classes of connected loopless simple graphs with maximum degree at most 3. - Brendan McKay, Mar 11 2020

Nino Bašić and Ivan Damnjanović, On cubic polycirculant nut graphs, arXiv:2411.16904 [math.CO], 2024. See p. 22.
Gunnar Brinkmann, Nico Van Cleemput, and Tomaž Pisanski, Generation of various classes of trivalent graphs, Theoretical Comp. Sci. (2013) Vol. 502, 16-29.

Cf. A121941, A243391, A243392, A243394, A303032.

a(24)-a(28) from Andrew Howroyd, Mar 20 2020

A243392 Number of isomorphism classes of connected 3-regular simple graphs of order 2n with loops and semi-edges allowed.

Original entry on oeis.org

2, 3, 4, 12, 22, 68, 166, 534, 1589, 5464, 18579, 68320, 255424, 1000852, 4018156, 16671976, 70890940, 309439942, 1381815168, 6310880471, 29428287639, 140012980007, 678970863717, 3353545264060, 16857749613964, 86191265140699, 447951112379963, 2365177154077186

Offset: 1

Nico Van Cleemput, Jun 04 2014

nonn

G. Brinkmann, N. Van Cleemput, T. Pisanski, Generation of various classes of trivalent graphs, Theoretical Computer Science 502, 2013, pp.16-29.

Differs from A243391 only in the first term.

a(23)-a(28) from Andrew Howroyd, May 06 2021

A243391 Number of isomorphism classes of connected 3-regular loopless multigraphs with n vertices and with semi-edges allowed.

Original entry on oeis.org

1, 3, 4, 12, 22, 68, 166, 534, 1589, 5464, 18579, 68320, 255424, 1000852, 4018156, 16671976, 70890940, 309439942, 1381815168, 6310880471, 29428287639, 140012980007, 678970863717, 3353545264060, 16857749613964, 86191265140699, 447951112379963, 2365177154077186

Offset: 1

Nico Van Cleemput, Jun 04 2014

nonn

a(n) is also the number of isomorphism classes of connected loopless multigraphs with n vertices of degree 3 or less. - Andrew Howroyd, Mar 20 2020

Nino Bašić and Ivan Damnjanović, On cubic polycirculant nut graphs, arXiv:2411.16904 [math.CO], 2024. See p. 22.
Gunnar Brinkmann, Nico Van Cleemput, and Tomaž Pisanski, Generation of various classes of trivalent graphs, Theoretical Comp. Sci. (2013) Vol. 502, 16-29.

Column k=3 of A334546.

Cf. A000421, A243392, A243393, A243394, A303030.

a(23)-a(28) from Andrew Howroyd, Mar 20 2020

A198086 Number of isomorphism classes of nanocones with 5 pentagons and a symmetric boundary of length n.

Original entry on oeis.org

1, 5, 14, 41, 93, 212, 413, 797, 1399, 2424, 3941, 6317, 9686, 14654, 21451, 31025, 43754, 61042, 83484, 113084, 150732, 199211, 259804, 336263, 430401, 547166, 689034, 862426, 1070653, 1321891, 1620501, 1976744, 2396247, 2891749, 3470397, 4147802, 4932954, 5844785, 6894435, 8104688, 9489198

Offset: 5

Nico Van Cleemput, Oct 21 2011

nonn

Nico Van Cleemput, Table of n, a(n) for n = 5..75
Gunnar Brinkmann and Nico Van Cleemput, Classification and generation of nanocones, Discrete Applied Mathematics, 159 (2011), 1528-1539.

Cf. A197988, A198014, A198015, A198016.

A198016 Number of isomorphism classes of nanocones with 4 pentagons and a nearsymmetric boundary of length n.

Original entry on oeis.org

2, 9, 32, 89, 204, 420, 786, 1376, 2272, 3589, 5450, 8021, 11474, 16032, 21928, 29452, 38902, 50645, 65056, 82585, 103692, 128920, 158822, 194044, 235240, 283165, 338586, 402377, 475422, 558724, 653296, 760276, 880814, 1016193, 1167708, 1336797, 1524908

Offset: 2

Nico Van Cleemput, Oct 20 2011

nonn

Nico Van Cleemput, Table of n, a(n) for n = 2..75
Gunnar Brinkmann and Nico Van Cleemput, Classification and generation of nanocones, Discrete Applied Mathematics, 159 (2011), 1528-1539.

Conjectured g.f.: x^2*(-2*x^8 + 5*x^7 + x^6 + 13*x^5 + 8*x^4 + 13*x^3 + 9*x^2 + 3*x + 2)/(x^12 - 3*x^11 + 2*x^10 + x^9 - x^8 + 2*x^7 - 4*x^6 + 2*x^5 - x^4 + x^3 + 2*x^2 - 3*x + 1). [D. S. McNeil, Oct 20 2011]

A198015 Number of isomorphism classes of nanocones with 4 pentagons and a symmetric boundary of length n.

Original entry on oeis.org

1, 4, 16, 37, 89, 175, 336, 579, 975, 1533, 2363, 3477, 5030, 7040, 9716, 13078, 17400, 22707, 29342, 37336, 47112, 58705, 72627, 88918, 108185, 130476, 156502, 186315, 220741, 259839, 304554, 354953, 412111, 476101, 548137, 628299, 717946, 817168, 927478

Offset: 2

Nico Van Cleemput, Oct 20 2011

nonn

Nico Van Cleemput, Table of n, a(n) for n = 2..75
G. Brinkmann and N. Van Cleemput, Classification and generation of nanocones, Discrete Applied Mathematics, 159 (2011), 1528-1539.

Conjectured g.f.: x^2*(-x^11 + x^10 - x^9 + 4*x^8 + 5*x^7 + 10*x^6 + 9*x^5 + 11*x^4 + 4*x^3 + 7*x^2 + 2*x + 1) / ((x - 1)^6*(x + 1)^3*(x^2 + 1)*(x^2 + x + 1)). [D. S. McNeil, Oct 20 2011]

A198014 Number of isomorphism classes of nanocones with 3 pentagons and a nearsymmetric boundary of length n.

Original entry on oeis.org

2, 8, 18, 37, 63, 104, 153, 224, 305, 413, 534, 688, 856, 1064, 1288, 1557, 1845, 2184, 2543, 2960, 3399, 3901, 4428, 5024, 5646, 6344, 7070, 7877, 8715, 9640, 10597, 11648, 12733, 13917, 15138, 16464, 17828, 19304, 20820, 22453, 24129, 25928, 27771, 29744

Offset: 1

Nico Van Cleemput, Oct 20 2011

nonn

Nico Van Cleemput, Table of n, a(n) for n = 1..75
Gunnar Brinkmann and Nico Van Cleemput, Classification and generation of nanocones, Discrete Applied Mathematics, 159 (2011), 1528-1539.

Conjectured g.f.: (3*x^5 + 2*x^4 + 5*x^3 + 6*x^2 + 6*x + 2)*x/((x - 1)^4*(x + 1)^2*(x^2 + x + 1)). [D. S. McNeil, Oct 20 2011]

A197988 Number of isomorphism classes of nanocones with 3 pentagons and a symmetric boundary of length n.

Original entry on oeis.org

1, 3, 5, 12, 18, 31, 44, 67, 88, 124, 157, 207, 255, 323, 387, 476, 560, 671, 778, 915, 1046, 1212, 1371, 1567, 1757, 1987, 2209, 2476, 2734, 3039, 3336, 3683, 4020, 4412, 4793, 5231, 5659, 6147, 6623, 7164, 7692, 8287, 8870, 9523, 10162, 10876, 11575, 12351

Offset: 1

Nico Van Cleemput, Oct 20 2011

nonn

Nico Van Cleemput, Table of n, a(n) for n = 1..75
Gunnar Brinkmann and Nico Van Cleemput, Classification and generation of nanocones, Discrete Applied Mathematics, 159 (2011), 1528-1539.

Conjectured g.f.: (x^7 + x^5 + x^4 + 2*x^3 + 2*x + 1)*x/((x - 1)^4*(x + 1)^2*(x^2 + x + 1)). [D. S. McNeil, Oct 20 2011]

cp's OEIS Frontend

User: Nico Van Cleemput

A243394 Number of isomorphism classes of connected 3-regular multigraphs with n vertices and with loops and semi-edges allowed.

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A243393 Number of isomorphism classes of connected 3-regular loopless simple graphs with n vertices and with semi-edges allowed.

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A243392 Number of isomorphism classes of connected 3-regular simple graphs of order 2n with loops and semi-edges allowed.

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A243391 Number of isomorphism classes of connected 3-regular loopless multigraphs with n vertices and with semi-edges allowed.

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Author

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A198086 Number of isomorphism classes of nanocones with 5 pentagons and a symmetric boundary of length n.

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A198016 Number of isomorphism classes of nanocones with 4 pentagons and a nearsymmetric boundary of length n.

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A198015 Number of isomorphism classes of nanocones with 4 pentagons and a symmetric boundary of length n.

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A198014 Number of isomorphism classes of nanocones with 3 pentagons and a nearsymmetric boundary of length n.

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A197988 Number of isomorphism classes of nanocones with 3 pentagons and a symmetric boundary of length n.

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