A001337 -id:A001337 - cp's OEIS frontend

A001336 Number of n-step self-avoiding walks on f.c.c. lattice.

1, 12, 132, 1404, 14700, 152532, 1573716, 16172148, 165697044, 1693773924, 17281929564, 176064704412, 1791455071068, 18208650297396, 184907370618612, 1876240018679868, 19024942249966812, 192794447005403916, 1952681556794601732, 19767824914170222996

Offset: 0

N. J. A. Sloane

B. D. Hughes, Random Walks and Random Environments, Oxford 1995, vol. 1, p. 460.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Andrey Zabolotskiy, Table of n, a(n) for n = 0..24 (from Schram et al.)
M. E. Fisher and M. F. Sykes, Excluded-volume problem and the Ising model of ferromagnetism, Phys. Rev. 114 (1959), 45-58.
B. D. Hughes, Random Walks and Random Environments, vol. 1, Oxford 1995, Tables and references for self-avoiding walks counts [Annotated scanned copy of several pages of a preprint or a draft of chapter 7 "The self-avoiding walk"]
J. L. Martin, M. F. Sykes and F. T. Hioe, Probability of initial ring closure for self-avoiding walks on the face-centered cubic and triangular lattices, J. Chem. Phys., 46 (1967), 3478-3481.
S. McKenzie, Self-avoiding walks on the face-centered cubic lattice, J. Phys. A 12 (1979), L267-L270.
S. Redner, Distribution functions in the interior of polymer chains, J. Phys. A 13 (1980), 3525-3541, doi:10.1088/0305-4470/13/11/023.
Raoul D. Schram, Gerard T. Barkema, Rob H. Bisseling and Nathan Clisby, Exact enumeration of self-avoiding walks on BCC and FCC lattices, J. Stat. Mech. (2017) 083208; arXiv:1703.09340 [cond-mat.stat-mech], 2017. See Table II.
M. F. Sykes, Some counting theorems in the theory of the Ising problem and the excluded volume problem, J. Math. Phys., 2 (1961), 52-62.
Index entries for sequences related to f.c.c. lattice

Cf. A001411, A001412, A001334, A001666, A001337.

a(15) from Bert Dobbelaere, Jan 13 2019

Terms a(16) and beyond from Schram et al. added by Andrey Zabolotskiy, Feb 02 2022

A003287 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,1,1).

Original entry on oeis.org

1, 4, 22, 140, 970, 7196, 56092, 452064, 3735700, 31484244, 269613896, 2339571468, 20529434520, 181871459580, 1624587752400, 14617165101216

Offset: 1

N. J. A. Sloane

Cf. A001337.

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

D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
Index entries for sequences related to f.c.c. lattice

Equals A001337(n+1) / 12 for n > 1.
Equals (n+1) * A005398(n+1) / 6 for n > 1.
Cf. A003288, A005543, A005544, A005545, A005546, A005547, A005548.

A001337 = Cases[Import["https://oeis.org/A001337/b001337.txt", "Table"], {, }][[All, 2]];
a[n_] := If[n == 1, 1, A001337[[n + 1]]/12];
a /@ Range[16] (* Jean-François Alcover, Jan 20 2020 *)

One more term and title improved by Sean A. Irvine, Feb 15 2016

a(15)-a(16) from Bert Dobbelaere, Jan 14 2019

A344070 Number of n-step self-avoiding cycles on the hypertriangular lattice.

Original entry on oeis.org

1, 0, 1, 1, 0, 5, 30, 77, 192, 879, 3860, 14102, 52916, 217295, 896252, 3631970, 14862624, 61811422, 258539856, 1084119347, 4568946800, 19360675922

Offset: 0

Sean A. Irvine, May 08 2021

Sean A. Irvine Java program (github)

Cf. A046945, A344039, A344071, A001337, A344126.

A344071 Number of 2n-step self-avoiding cycles on the Laves graph.

Original entry on oeis.org

1, 1, 0, 0, 0, 10, 0, 14, 112, 282, 600, 2618, 9400, 27378, 93828, 332070, 1127840, 3818438, 13369560, 46776898, 163073440, 572984748, 2026468708, 7176533646

Offset: 0

Sean A. Irvine, May 09 2021

Sean A. Irvine, Java program (github)
Wikipedia, Laves graph

Cf. A046944, A344040, A344070, A001337, A038620.

Name clarified by Andrey Zabolotskiy, Jun 03 2021

A038515 Number of self-avoiding walks on a tetrahedral (diamond) net, having 2n steps and forming a closed loop.

Original entry on oeis.org

1, 0, 0, 6, 12, 120, 564, 4074, 25008, 174618, 1181100, 8358306, 59167872, 427081512, 3103408308, 22797207330, 168616517760, 1256350493196

Offset: 0

Wouter Meeussen

Anthony J. Guttmann and Iwan Jensen, Appendix: Series Data and Growth Constant, Amplitude and Exponent Estimates, in: Polygons, Polyominoes and Polycubes, LNP 775, Springer, 2009. See Table 16.12 on p. 480 for the sequence a(n)/n.
Sean A. Irvine, Java program (github)

Cf. A001394, A001667, A001413, A001337, A344070, A344071.

a(0)=1 and a(9)-a(15) from Sean A. Irvine, Jan 16 2021

a(16)-a(17) using the data from Guttmann & Jensen added by Andrey Zabolotskiy, Jun 02 2022

A005398 Number of n-step polygons on f.c.c. lattice.

Original entry on oeis.org

8, 33, 168, 970, 6168, 42069, 301376, 2241420, 17173224, 134806948, 1079802216, 8798329080, 72748583832, 609220407150, 5158999447488

Offset: 3

N. J. A. Sloane

A. J. Guttmann, Polygons, Polyominoes and Polycubes, Lecture Notes in Physics Volume 775, 2009, Chapter 16.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

M. F. Sykes et al., Lattice constant systems and graph theory, J. Math. Phys., 7 (1966), 1557-1572.
Index entries for sequences related to f.c.c. lattice

Equals A001337(n) / (2n).

A001337 = Cases[Import["https://oeis.org/A001337/b001337.txt", "Table"], {, }][[All, 2]];
a[n_] := A001337[[n]]/(2n);
a /@ Range[3, 17] (* Jean-François Alcover, Jan 20 2020 *)

More terms from Ruperto Corso, Dec 19 2011
a(15) and a(16) from Sean A. Irvine, Mar 30 2017
a(17) from Bert Dobbelaere, Jan 14 2019

A001667 2n-step polygons on b.c.c. lattice.

Original entry on oeis.org

96, 1776, 43776, 1237920, 37903776, 1223681760, 41040797376, 1416762272736, 50027402384640, 1799035070369856

Offset: 2

N. J. A. Sloane

Number of 2n-step closed self-avoiding walks starting from the origin. - Bert Dobbelaere, Jan 16 2019

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

P. Butera and M. Comi, Enumeration of the self-avoiding polygons on a lattice by the Schwinger-Dyson equations, Annals of Combinatorics 3, 277-286 (1999); arXiv:cond-mat/9903297, 1999.
M. E. Fisher and M. F. Sykes, Excluded-volume problem and the Ising model of ferromagnetism, Phys. Rev. 114 (1959), 45-58.
M. F. Sykes et al., The number of self-avoiding walks on a lattice, J. Phys. A 5 (1972), 661-666.
Index entries for sequences related to b.c.c. lattice

Cf. A001666, A001413, A001337, A038515.

a(9)-a(10) from Bert Dobbelaere, Jan 16 2019

a(11) from Butera & Comi added by Andrey Zabolotskiy, Jun 02 2022

cp's OEIS Frontend

A001336 Number of n-step self-avoiding walks on f.c.c. lattice.

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A003287 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,1,1).

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A344070 Number of n-step self-avoiding cycles on the hypertriangular lattice.

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A344071 Number of 2n-step self-avoiding cycles on the Laves graph.

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A038515 Number of self-avoiding walks on a tetrahedral (diamond) net, having 2n steps and forming a closed loop.

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A005398 Number of n-step polygons on f.c.c. lattice.

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A001667 2n-step polygons on b.c.c. lattice.

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