A007181 Expansion of critical exponent for walks on tetrahedral lattice. (Formerly M0340)

2, 2, 4, 12, 30, 60, 154, 404, 1046, 2540, 6720, 17484, 46522, 120300, 323800, 856032, 2315578, 6151080, 16745530, 44921984, 122790698, 331148108, 908909558, 2465359580, 6788313198, 18491757632, 51067082988

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 for all points and t = z for the final point. - Sean A. Irvine, Nov 11 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: A285611 A288303 A287604 * A100238 A208529 A212660

Adjacent sequences: A007178 A007179 A007180 * A007182 A007183 A007184

Keyword

nonn,walk

Author

Simon Plouffe

Extensions

a(21)-a(27) from Sean A. Irvine, Nov 11 2017

Status

approved