A006736 -id:A006736 - cp's OEIS frontend

A006809 Bond percolation series for hexagonal lattice.

1, 3, 9, 25, 66, 168, 417, 1014, 2427, 5737, 13412, 31088, 71506, 163378, 371272, 839248, 1889019, 4235082, 9459687, 21067566, 46769977, 103574916, 228808544, 504286803, 1109344029, 2435398781, 5337497418, 11678931098

Offset: 0

N. J. A. Sloane, Simon Plouffe

sign

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

The first negative term occurs at index 89.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

I. Jensen, Table of n, a(n) for n = 0..90 (from link below)
J. Blease, Series expansions for the directed-bond percolation problem, J. Phys. C 10 (1977), 917-924.
J. W. Essam, A. J. Guttmann and K. De'Bell, On two-dimensional directed percolation, J. Phys. A 21 (1988), 3815-3832.
I. Jensen, More terms
Iwan Jensen, Anthony J. Guttmann, Series expansions of the percolation probability for directed square and honeycomb lattices, J. Phys. A 28 (1995), no. 17, 4813-4833.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

Cf. A006803, A006736.

A006737 Series for second parallel moment of hexagonal lattice.

Original entry on oeis.org

0, 6, 68, 442, 2218, 9528, 36834, 131856, 445000, 1433294, 4444006, 13349510, 39041224, 111583236, 312618368, 860662498, 2333112020, 6238124024, 16474149036, 43023953304, 111230237224, 284926172100, 723731637254

Offset: 0

N. J. A. Sloane, Simon Plouffe

nonn

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

I. Jensen, Table of n, a(n) for n = 0..90 (from link below)
I. G. Enting, A, J. Guttmann and I. Jensen, Low-Temperature Series Expansions for the Spin-1 Ising Model, arXiv:hep-lat/9410005, 1994; J. Phys. A. 27 (1994) 6987-7006.
J. W. Essam, A. J. Guttmann and K. De'Bell, On two-dimensional directed percolation, J. Phys. A 21 (1988), 3815-3832.
I. Jensen, More terms
Iwan Jensen, Anthony J. Guttmann, Series expansions of the percolation probability for directed square and honeycomb lattices, arXiv:cond-mat/9509121, 1995; J. Phys. A 28 (1995), no. 17, 4813-4833.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

Cf. A006803, A006809, A006736, A006738.

A006738 Series for second perpendicular moment of hexagonal lattice.

Original entry on oeis.org

0, 2, 12, 54, 206, 712, 2294, 7024, 20656, 58842, 163250, 443062, 1180156, 3092964, 7993116, 20401250, 51502616, 128748512, 319010540, 784179992, 1913668608, 4639155964, 11178566462, 26784974870, 63851541584

Offset: 0

N. J. A. Sloane, Simon Plouffe

nonn

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

I. Jensen, Table of n, a(n) for n = 0..90 (from link below)
I. G. Enting, A, J. Guttmann and I. Jensen, Low-Temperature Series Expansions for the Spin-1 Ising Model, arXiv:hep-lat/9410005, 1994; J. Phys. A. 27 (1994) 6987-7006.
J. W. Essam, A. J. Guttmann and K. De'Bell, On two-dimensional directed percolation, J. Phys. A 21 (1988), 3815-3832.
I. Jensen, More terms
Iwan Jensen, Anthony J. Guttmann, Series expansions of the percolation probability for directed square and honeycomb lattices, arXiv:cond-mat/9509121, 1995; J. Phys. A 28 (1995), no. 17, 4813-4833.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

Cf. A006803, A006809, A006736, A006737.

cp's OEIS Frontend

A006809 Bond percolation series for hexagonal lattice.

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A006737 Series for second parallel moment of hexagonal lattice.

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Author

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Comments

References

Links

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A006738 Series for second perpendicular moment of hexagonal lattice.

Views

Author

Keywords

Comments

References

Links

Crossrefs