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A116904
Number of n-step self-avoiding walks on the upper 4 octants of the cubic grid starting at origin.
11
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
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
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