A082640 -id:A082640 - cp's OEIS frontend

A151686 Row sums of A082640.

2, 70, 47328, 739818456, 260629633975688, 1999548813009227307620, 332646010718562425157153825748, 1191074182322287023188471842472410738322, 91376667433034677542811906990191155440283816809920

Offset: 1

N. J. A. Sloane, Jun 02 2009

Typo in name corrected by Francisco Santos, Nov 07 2016

a(7)-a(9) from Stepan Orevkov, Feb 08 2022

A351484 a(n) is the number of primitive triangulations of a 5 X n rectangle.

Original entry on oeis.org

252, 182132, 182881520, 208902766788, 260420548144996, 341816489625522032, 464476385680935656240, 645855159466371391947660, 913036902513499041820702784, 1306520849733616781789190513820, 1887591165891651253904039432371172, 2747848427721241461905176361078147168

Offset: 1

Stefano Spezia, Feb 12 2022

nonn

S. Yu. Orevkov, Counting lattice triangulations: Fredholm equations in combinatorics, arXiv:2201.12827 [math.CO], 2022. See Table 2, p. 6.

Cf. A082640 (m X n rectangle).
Cf. A351480, A351481, A351482, A351483.
Cf. A351485, A351486, A351487, A351488.

A351485 a(n) is the number of primitive triangulations of a 6 X n rectangle.

Original entry on oeis.org

924, 2801708, 12244184472, 61756221742966, 341816489625522032, 1999206934751133055518, 12169409954141988707186052, 76083336332947513655554918994, 484772512167266688498399632918196, 3131521959869770128138491287826065904, 20443767611927599823217291769468449488548

Offset: 1

Stefano Spezia, Feb 12 2022

nonn

S. Yu. Orevkov, Counting lattice triangulations: Fredholm equations in combinatorics, arXiv:2201.12827 [math.CO], 2022. See Table 3, p. 7.

Cf. A082640 (m X n rectangle).
Cf. A351480, A351481, A351482, A351483.
Cf. A351484, A351486, A351487, A351488.

A351486 a(n) is the number of primitive triangulations of a 7 X n rectangle.

Original entry on oeis.org

3432, 43936824, 839660660268, 18792896208387012, 464476385680935656240, 12169409954141988707186052, 332633840844113103751597995920, 9369363517501208819530429967280708, 269621109753732518252493257828413137272, 7880009979020501614060394747170100093057300, 233031642883906149386619647304562977586311372556

Offset: 1

Stefano Spezia, Feb 12 2022

nonn

S. Yu. Orevkov, Counting lattice triangulations: Fredholm equations in combinatorics, arXiv:2201.12827 [math.CO], 2022. See Table 4, p. 7.

Cf. A082640 (m X n rectangle).
Cf. A351480, A351481, A351482, A351483.
Cf. A351484, A351485, A351487, A351488.

A351487 a(n) is the number of primitive triangulations of an 8 X n rectangle.

Original entry on oeis.org

12870, 698607816, 58591381296256, 5831528022482629710, 645855159466371391947660, 76083336332947513655554918994, 9369363517501208819530429967280708, 1191064812882685539785713745400934044308, 155023302820254133629368881178138076738462112, 20527337238769032315796332007167102984745417344046

Offset: 1

Stefano Spezia, Feb 12 2022

nonn

S. Yu. Orevkov, Counting lattice triangulations: Fredholm equations in combinatorics, arXiv:2201.12827 [math.CO], 2022. See Table 5, p. 8.

Cf. A082640 (m X n rectangle).
Cf. A351480, A351481, A351482, A351483.
Cf. A351484, A351485, A351486, A351488.

A351488 a(n) is the number of primitive triangulations of a 9 X n rectangle.

Original entry on oeis.org

48620, 11224598424, 4140106747178292, 1835933384812941453312, 913036902513499041820702784, 484772512167266688498399632918196, 269621109753732518252493257828413137272, 155023302820254133629368881178138076738462112, 91376512409462235694151119897052344522006298310908

Offset: 1

Stefano Spezia, Feb 12 2022

nonn

S. Yu. Orevkov, Counting lattice triangulations: Fredholm equations in combinatorics, arXiv:2201.12827 [math.CO], 2022. See Table 6, p. 8.

Cf. A082640 (m X n rectangle).
Cf. A351480, A351481, A351482, A351483.
Cf. A351484, A351485, A351486, A351487.

A351480 Decimal expansion of (611 + sqrt(73))/36.

Original entry on oeis.org

1, 7, 2, 0, 9, 5, 5, 5, 6, 5, 9, 5, 9, 2, 1, 5, 3, 6, 4, 3, 5, 5, 1, 9, 9, 0, 2, 3, 1, 2, 8, 4, 4, 3, 6, 2, 8, 9, 8, 4, 9, 8, 4, 5, 9, 8, 1, 3, 7, 5, 9, 2, 4, 5, 0, 6, 7, 1, 9, 6, 8, 4, 7, 5, 7, 0, 4, 9, 2, 1, 2, 4, 6, 7, 2, 0, 3, 5, 3, 6, 0, 6, 6, 1, 4, 1, 1, 3, 8, 1

Offset: 2

Stefano Spezia, Feb 12 2022

			17.2095556595921536435519902312844...

S. Yu. Orevkov, Counting lattice triangulations: Fredholm equations in combinatorics, arXiv:2201.12827 [math.CO], 2022. See Theorem 1, p. 2.
Index entries for algebraic numbers, degree 2

Cf. A010525, A082640.
Cf. A351481, A351482, A351483.
Cf. A351484, A351485, A351486, A351487, A351488.

First[RealDigits[(611+Sqrt[73])/36,10,90]]

Equals lim_{n->oo} A082640(2, n)^(1/n).

Equals 288*x_2, where x_2 is the largest root of 5184*x^2 - 611*x + 18.

A351481 Decimal expansion of log_2((611 + sqrt(73))/36)/2.

Original entry on oeis.org

2, 0, 5, 2, 5, 6, 8, 9, 7, 1, 6, 1, 2, 7, 3, 5, 6, 6, 5, 1, 0, 7, 8, 7, 1, 5, 4, 0, 4, 7, 8, 6, 5, 5, 8, 7, 1, 0, 5, 3, 8, 4, 8, 7, 6, 2, 3, 7, 1, 2, 2, 1, 4, 3, 8, 8, 9, 2, 9, 8, 0, 3, 2, 7, 7, 4, 1, 7, 9, 0, 8, 2, 0, 0, 4, 1, 2, 0, 7, 1, 0, 4, 6, 5, 9, 3, 2, 3, 6, 3

Offset: 1

Stefano Spezia, Feb 12 2022

			2.052568971612735665107871540478655871...

S. Yu. Orevkov, Counting lattice triangulations: Fredholm equations in combinatorics, arXiv:2201.12827 [math.CO], 2022. See Theorem 1, p. 2.
Index entries for transcendental numbers

Cf. A010525, A082640.
Cf. A351480, A351482, A351483.
Cf. A351484, A351485, A351486, A351487, A351488.

First[RealDigits[N[Log[2,(611+Sqrt[73])/36]/2,90]]]

log((611 + sqrt(73))/36)/log(4) \\ Charles R Greathouse IV, Oct 31 2023

Equals log_2(alpha)/2, where alpha = lim_{n->oo} A082640(2, n)^(1/n).

A351482 Decimal expansion of lim_{n->oo} f(3, n)^(1/(3*n)), where f(m, n) is the number of primitive lattice triangulations of m X n rectangle.

Original entry on oeis.org

4, 2, 3, 9, 3, 6, 9, 4, 8, 1, 5, 4, 8, 0, 2, 5, 6, 7, 1, 8, 7, 7, 6, 2, 5, 7, 4, 2, 0, 4, 5, 2, 3, 5, 7, 7, 2, 1, 0, 0, 6, 9, 5, 7, 1, 1, 2, 5, 1, 7, 9, 5, 4, 9, 9, 8, 3, 0, 8, 0, 1, 6, 8, 7, 8, 3, 3, 3, 5, 8, 2, 3, 8, 2, 7, 6, 7, 2, 8, 9, 8, 7, 8, 3, 7, 0, 5, 4, 8

Offset: 1

Stefano Spezia, Feb 12 2022

			4.2393694815480256718776257420452357721...

S. Yu. Orevkov, Counting lattice triangulations: Fredholm equations in combinatorics, arXiv:2201.12827 [math.CO], 2022. See Theorem 2, p. 2.

Cf. A082640.
Cf. A351480, A351481, A351483.
Cf. A351484, A351485, A351486, A351487, A351488.

A351483 Decimal expansion of log_2(lim_{n->oo} f(3, n)^(1/(3*n))), where f(m, n) is the number of primitive lattice triangulations of m X n rectangle.

Original entry on oeis.org

2, 0, 8, 3, 8, 4, 9, 7, 0, 9, 7, 2, 1, 0, 2, 3, 2, 0, 8, 2, 2, 4, 2, 1, 9, 2, 8, 9, 4, 9, 6, 1, 7, 0, 1, 3, 9, 6, 4, 8, 5, 1, 3, 4, 2, 3, 2, 4, 9, 5, 5, 2, 1, 3, 0, 7, 9, 9, 0, 5, 9, 9, 1, 8, 5, 5, 1, 7, 2, 9, 0, 6, 9, 2, 8, 1, 8, 0, 5, 2, 5, 1, 8, 6, 6, 5, 0, 8, 8

Offset: 1

Stefano Spezia, Feb 12 2022

			2.0838497097210232082242192894961701...

S. Yu. Orevkov, Counting lattice triangulations: Fredholm equations in combinatorics, arXiv:2201.12827 [math.CO], 2022. See Theorem 2, p. 2.

Cf. A082640.
Cf. A351480, A351481, A351482.
Cf. A351484, A351485, A351486, A351487, A351488.

cp's OEIS Frontend

A151686 Row sums of A082640.

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A351484 a(n) is the number of primitive triangulations of a 5 X n rectangle.

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A351485 a(n) is the number of primitive triangulations of a 6 X n rectangle.

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A351486 a(n) is the number of primitive triangulations of a 7 X n rectangle.

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A351487 a(n) is the number of primitive triangulations of an 8 X n rectangle.

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A351488 a(n) is the number of primitive triangulations of a 9 X n rectangle.

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A351480 Decimal expansion of (611 + sqrt(73))/36.

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A351481 Decimal expansion of log_2((611 + sqrt(73))/36)/2.

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A351482 Decimal expansion of lim_{n->oo} f(3, n)^(1/(3*n)), where f(m, n) is the number of primitive lattice triangulations of m X n rectangle.

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A351483 Decimal expansion of log_2(lim_{n->oo} f(3, n)^(1/(3*n))), where f(m, n) is the number of primitive lattice triangulations of m X n rectangle.

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