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

Author

Giovanni Resta, Feb 15 2006

Keywords

• nonn

Comments

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

Examples

			See A116903 for a graphical example of the bidimensional counterpart.
		

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.

Crossrefs

Cf. A001412, A039648, A116903.

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