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A116904 Number of n-step self-avoiding walks on the upper 4 octants 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 (list; graph; refs; listen; history; text; internal format)
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..20.

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. [Vladeta Jovovic, Nov 26 2008]

T. Dachraoui et al., Elementary paths in a cubic lattice and application to molecular biology, Kybernetes, Vol. 26 No. 9, pp. 1012-1030. [Vladeta Jovovic, Nov 26 2008]

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,more

AUTHOR

Giovanni Resta, Feb 15 2006

EXTENSIONS

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

STATUS

approved

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Last modified December 5 12:01 EST 2022. Contains 358586 sequences. (Running on oeis4.)