|
| |
|
|
A001668
|
|
Number of self-avoiding n-step walks on honeycomb lattice.
(Formerly M2559 N1013)
|
|
3
| |
|
|
1, 3, 6, 12, 24, 48, 90, 174, 336, 648, 1218, 2328, 4416, 8388, 15780, 29892, 56268, 106200, 199350, 375504, 704304, 1323996, 2479692, 4654464, 8710212, 16328220, 30526374, 57161568, 106794084, 199788408, 372996450, 697217994, 1300954248
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| M. E. Fisher and M. F. Sykes, Excluded-volume problem and the Ising model of ferromagnetism, Phys. Rev. 114 (1959), 45-58.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. F. Sykes, Some counting theorems in the theory of the Ising problem and the excluded volume problem, J. Math. Phys., 2 (1961), 52-62.
M. F. Sykes et al., The asymptotic behavior of selfavoiding walks and returns on a lattice, J. Phys. A 5 (1972), 653-660.
|
|
|
LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..43
H. Duminil-Copin and S. Smirnov, The connective constant of the honeycomb lattice equals sqrt(2+sqrt(2)) (arXiv:1007.0575v2)
D. MacDonald, D. L. Hunter, K. Kelly and N. Jan, Self-avoiding walks in two to five dimensions: exact enumerations and series study, J Phys A: Math Gen 25 (1992) 1429-1440. [Gives 42 terms]
|
|
|
MAPLE
| a:= proc(n) local v, b;
if n<2 then return 1 +2*n fi;
v:= proc() false end: v(0, 0), v(1, 0):= true$2;
b:= proc(n, x, y) local c;
if v(x, y) then 0
elif n=0 then 1
else v(x, y):= true;
c:= b(n-1, x+1, y) + b(n-1, x-1, y) +
b(n-1, x, y-1+2*((x+y) mod 2));
v(x, y):= false; c
fi
end;
6*b(n-2, 1, 1)
end:
seq (a(n), n=0..20); # Alois P. Heinz, Jul 7 2011
|
|
|
CROSSREFS
| Cf. A006851.
Sequence in context: A102255 A192871 A002910 * A080616 A090572 A163876
Adjacent sequences: A001665 A001666 A001667 * A001669 A001670 A001671
|
|
|
KEYWORD
| nonn,walk,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Sykes et al. give 34 terms.
More terms from Pab Ter (pabrlos(AT)yahoo.com), May 06 2004
|
| |
|
|
