Anthony Guttmann - cp's OEIS frontend

A356610 Number of SAWs crossing a rhomboidal domain of the hexagonal lattice.

2, 14, 316, 25092, 7374480, 8029311942, 32223151155864, 476605408516689238, 26016526700583361056456, 5246595079903462547245876694, 3911053741699230141571030313824664, 10780907768757190963361134040036893772360, 109919900687141309301630828947780890728732496678

Offset: 1

Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022

nonn

Anthony J. Guttmann, Table of n, a(n) for n = 1..26
Anthony J. Guttmann and Iwan Jensen, Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices, arXiv:2208.06744 [math-ph], Aug 13 2022, Table D3.

Cf. A001006, A002026, A007764, A116485.

A356611 Number of SAWs spanning a rhomboidal domain of the hexagonal lattice.

Original entry on oeis.org

2, 50, 2256, 292006, 124394172, 182189852062, 937116505296162, 17167376550995687961, 1130911800993488803731078, 269650395624478266477331223678, 233772496350603982679550385266064014, 739330863241806743025423160490836132227125, 8551000409049037000098287028025432585191736309022

Offset: 1

Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022

nonn

Anthony J. Guttmann, Table of n, a(n) for n = 1..26
Anthony J. Guttmann and Iwan Jensen, Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices, arXiv:2208.06744 [math-ph], Aug 13 2022, Table D4.

Cf. A001006, A002026, A007764, A116485.

A356612 Number of SAPs crossing a rhomboidal domain of the hexagonal lattice.

Original entry on oeis.org

1, 3, 48, 3126, 775842, 727870836, 2575728525240, 34244061451559094, 1703999058661009145746, 316543880488539946466963896, 219157996022284922702859434801868, 564858713948847373563461482383973674774, 5415142061627863782256892670635702203299498106

Offset: 1

Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022

nonn

Anthony J. Guttmann, Table of n, a(n) for n = 1..26
Anthony J. Guttmann and Iwan Jensen, Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices, arXiv:2208.06744 [math-ph], Aug 13 2022, Table D5.

Cf. A001006, A002026, A007764, A116485.

A356613 Number of SAWs crossing a triangular domain of the hexagonal lattice.

Original entry on oeis.org

2, 7, 44, 515, 11500, 493704, 40751496, 6463642330, 1970190022696, 1154437344815284, 1300686960810345198, 2818300749120970598426, 11745284697899678209887246, 94153940687296424300453605522, 1451915619132744566900848537333082, 43072062058620235613855525243039798546

Offset: 1

Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022

nonn

Anthony J. Guttmann, Table of n, a(n) for n = 1..27
Anthony J. Guttmann and Iwan Jensen, Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices, arXiv:2208.06744 [math-ph], Aug 13 2022, Table D6.

Cf. A001006, A002026, A007764, A116485.

A356614 Number of SAWs crossing a triangular domain of the hexagonal lattice and including the top vertex.

Original entry on oeis.org

1, 3, 18, 210, 4716, 203130, 16781528, 2661898722, 811337884328, 475395297020430, 535618774376758222, 1160567857061063474508, 4836675324919658534327348, 38772333263059858336182467950, 597894854584620490267288203881970, 17736956492510173648327596231133813426

Offset: 1

Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022

nonn

Anthony J. Guttmann, Table of n, a(n) for n = 1..26
Anthony J. Guttmann and Iwan Jensen, Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices, arXiv:2208.06744 [math-ph], Aug 13 2022, Table D7.

Cf. A001006, A002026, A007764, A116485.

A356615 Number of SAPs crossing a triangular domain of the hexagonal lattice.

Original entry on oeis.org

1, 2, 9, 85, 1605, 59896, 4392639, 629739138, 175745776816, 95207239875508, 99934927799315359, 202993550188918062298, 797200289814680588454420, 6048794511036987586252009778, 88623124229469033988344357343229, 2506168305598107863294101582119745559

Offset: 1

Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022

nonn

Anthony J. Guttmann, Table of n, a(n) for n = 1..26
Anthony J. Guttmann and Iwan Jensen, Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices, arXiv:2208.06744 [math-ph], Aug 13 2022, Table D8.

Cf. A001006, A002026, A007764, A116485.

A356616 Number of SAPs crossing a triangular domain of the hexagonal lattice and including top vertex.

Original entry on oeis.org

1, 1, 4, 36, 666, 24696, 1808820, 259300148, 72369408510, 39205936157880, 41152969216872016, 83592236529606631688, 328284931491454739745904, 2490876950205850778116435156, 36494758452603010620499864088198, 1032033208911845667821292289616451218

Offset: 1

Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022

nonn

Anthony J. Guttmann, Table of n, a(n) for n = 1..26
Anthony J. Guttmann and Iwan Jensen, Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices, arXiv:2208.06744 [math-ph], Aug 13 2022, Table D9.

Cf. A001006, A002026, A007764, A116485.

A356617 Number of square lattice worms w_n.

Original entry on oeis.org

1, 1, 3, 7, 19, 41, 113, 261, 713, 1681, 4567, 10993, 29717, 72493, 195269, 481261, 1292729, 3211263, 8606801, 21515135, 57561815, 144631085, 386382359, 974968645, 2601469419, 6587913395, 17560287513, 44605607915, 118794020215, 302552020141, 805154546027

Offset: 1

Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022

nonn

Anthony J. Guttmann, Table of n, a(n) for n = 1..59
Anthony J. Guttmann and Iwan Jensen, On the existence of critical exponents for self-avoiding walks, arXiv:2207.08433 [math-ph], Jul 18 2022, Table 1, p. 12.

A356618 Number of triangular lattice worms w_n.

Original entry on oeis.org

1, 3, 11, 41, 155, 603, 2361, 9321, 37015, 147657, 591227, 2374539, 9561487, 38585555, 156007667, 631806555, 2562434223, 10405918209, 42306525037, 172180092143, 701397054549, 2859651782649, 11668050956347, 47642140547239, 194655761552949, 795800965884627

Offset: 1

Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022

nonn

Anthony J. Guttmann, Table of n, a(n) for n = 1..40
Anthony J. Guttmann and Iwan Jensen, On the existence of critical exponents for self-avoiding walks, arXiv:2207.08433 [math-ph], Jul 18 2022, Table 1, p. 12.

A348925 Number of 4-sided prudent polygons of area n.

Original entry on oeis.org

8, 16, 40, 96, 232, 560, 1336, 3176, 7480, 17528, 40776, 94336, 216976, 496432, 1130120, 2560648, 5776304, 12976112, 29036008, 64732992, 143814192, 318455632, 702983256, 1547254832, 3395989288, 7433962168, 16232357608, 35359307144, 76848753032, 166658534216

Offset: 1

Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Nov 04 2021

nonn

Nicholas R. Beaton and Anthony Guttmann, Table of n, a(n) for n = 1..800
Nicholas R. Beaton, Philippe Flajolet, Tim Garoni and Anthony J. Guttmann, Some New Self-avoiding Walk and Polygon Models, Fundamenta Informaticae, vol. 117, 2012, pp. 19-33.
Nicholas R. Beaton, Philippe Flajolet and Anthony J. Guttmann, The Enumeration of Prudent Polygons by Area and its Unusual Asymptotics, arXiv:1011.6195 [math.CO], Nov 29 2010, updated Nov 04 2021.

Cf. A052548, A348838.

cp's OEIS Frontend

User: Anthony Guttmann

A356610 Number of SAWs crossing a rhomboidal domain of the hexagonal lattice.

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A356611 Number of SAWs spanning a rhomboidal domain of the hexagonal lattice.

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A356612 Number of SAPs crossing a rhomboidal domain of the hexagonal lattice.

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A356613 Number of SAWs crossing a triangular domain of the hexagonal lattice.

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A356614 Number of SAWs crossing a triangular domain of the hexagonal lattice and including the top vertex.

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A356615 Number of SAPs crossing a triangular domain of the hexagonal lattice.

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A356616 Number of SAPs crossing a triangular domain of the hexagonal lattice and including top vertex.

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A356617 Number of square lattice worms w_n.

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A356618 Number of triangular lattice worms w_n.

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A348925 Number of 4-sided prudent polygons of area n.

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