A116904 Number of n-step self-avoiding walks on the upper 4 octants of the cubic grid starting at origin.

1, 5, 21, 93, 409, 1853, 8333, 37965, 172265, 787557, 3593465, 16477845, 75481105, 346960613, 1593924045, 7341070889, 33798930541, 155915787353, 719101961769, 3321659652529, 15341586477457, 70944927549085, 328054694768261, 1518490945278377, 7028570356547189, 32560476643826933, 150838831585499069

Offset

0,2

Comments

Guttmann-Torrie simple cubic lattice series coefficients c_n^{2}(Pi). - N. J. A. Sloane, Jul 06 2015

Links

Table of n, a(n) for n=0..26.

M. N. Barber et al., Some tests of scaling theory for a self-avoiding walk attached to a surface, 1978 J. Phys. A: Math. Gen. 11 1833.

Nathan Clisby, Andrew R. Conway and Anthony J. Guttmann, Three-dimensional terminally attached self-avoiding walks and bridges, J. Phys. A: Math. Theor., 49 (2016), 015004; arXiv:1504.02085 [cond-mat.stat-mech], 2015. [Warning: arXiv version has typos in a(11) and a(12).]

T. Dachraoui et al., Elementary paths in a cubic lattice and application to molecular biology, Kybernetes, Vol. 26 No. 9, pp. 1012-1030.

A. J. Guttmann and G. M. Torrie, Critical behavior at an edge for the SAW and Ising model, J. Phys. A 17 (1984), 3539-3552.

Example

See A116903 for a graphical example of the bidimensional counterpart.

Crossrefs

Cf. A001412, A039648, A116903.

Sequence in context: A218964 A154964 A007287 * A126952 A273570 A103519

Adjacent sequences: A116901 A116902 A116903 * A116905 A116906 A116907

Keyword

nonn

Author

Giovanni Resta, Feb 15 2006

Extensions

a(16)-a(20) from Scott R. Shannon, Aug 12 2020

a(21)-a(26) from Clisby et al. added by Andrey Zabolotskiy, Apr 18 2023

Status

approved