login
Expansion of critical exponent for walks on tetrahedral lattice.
(Formerly M2674)
0

%I M2674 #17 Nov 12 2017 03:08:26

%S 3,7,19,53,147,401,1123,3137,8793,24599,69287,194967,550361,1552645,

%T 4393021,12425121,35213027,99771855,283162701,803538483,2283184527,

%U 6486977223,18450767769,52477038631,149387309235,425257329235,1211493474199

%N Expansion of critical exponent for walks on tetrahedral lattice.

%C 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

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

%H T. Ishinabe and S. G. Whittington, <a href="https://doi.org/10.1088/0305-4470/14/2/019">Surface critical exponents for self-avoiding walks on the tetrahedral lattice</a>, J. Phys. A 14 (1981), 439-446.

%K nonn,walk

%O 1,1

%A _Simon Plouffe_

%E a(20)-a(27) from _Sean A. Irvine_, Nov 10 2017