A007180 Expansion of critical exponent for walks on tetrahedral lattice. (Formerly M2674)

3, 7, 19, 53, 147, 401, 1123, 3137, 8793, 24599, 69287, 194967, 550361, 1552645, 4393021, 12425121, 35213027, 99771855, 283162701, 803538483, 2283184527, 6486977223, 18450767769, 52477038631, 149387309235, 425257329235, 1211493474199

Offset

1,1

Comments

Using coordinates (x,y,z,t) such that x+y+z+t = 0 or 1, then the four neighbors of (x,y,z,t) are found by changing one coordinate by +- 1 (such that the sum of coordinates remains 0 or 1). This sequence gives the number of self-avoiding walks of length n starting from (0,0,0,0) such that t <= z. - Sean A. Irvine, Nov 10 2017

References

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

Links

Table of n, a(n) for n=1..27.

T. Ishinabe and S. G. Whittington, Surface critical exponents for self-avoiding walks on the tetrahedral lattice, J. Phys. A 14 (1981), 439-446.

Crossrefs

Sequence in context: A259812 A115254 A222324 * A090378 A059506 A007575

Adjacent sequences: A007177 A007178 A007179 * A007181 A007182 A007183

Keyword

nonn,walk

Author

Simon Plouffe

Extensions

a(20)-a(27) from Sean A. Irvine, Nov 10 2017

Status

approved