A000511 Number of n-step spiral self-avoiding walks on hexagonal lattice, where at each step one may continue in same direction or make turn of 2*Pi/3 counterclockwise.

1, 1, 2, 3, 5, 8, 11, 17, 25, 33, 47, 67, 87, 117, 160, 207, 270, 356, 455, 584, 751, 945, 1195, 1513, 1882, 2345, 2927, 3608, 4446, 5483, 6701, 8180, 9986, 12109, 14664, 17750, 21371, 25694, 30872, 36937, 44127, 52672, 62658, 74429, 88327, 104524, 123518, 145819, 171737, 201990, 237332, 278289, 325901, 381278, 445272, 519381, 605230, 704170, 818357, 950150, 1101634, 1275907, 1476384, 1706226, 1969869, 2272224, 2618007, 3013559, 3465917, 3982025, 4570898, 5242569, 6007170, 6877474, 7867709, 8992510, 10269905, 11719991, 13363733, 15226469, 17336450, 19723485, 22423058, 25474712, 28920541, 32810028, 37198284, 42144403, 47717124, 53992936, 61054313, 68996364, 77924848, 87954283, 99215750, 111854888

Offset: 0

Author

Stephen Penrice (penrice(AT)dimacs.rutgers.edu)

Keywords

• nonn
• walk

Comments

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

Links

• J. H. Bruinier, Infinite products in number theory and geometry, arXiv:math/0404427 [math.NT], 2004.
• G. S. Joyce and R. Bak, An exact solution for a spiral self-avoiding walk model on the triangular lattice, J. Phys. A: Math. Gen. 18 (1985) L293-L298, esp. p. L297.
• G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

Extensions

More terms from Sean A. Irvine, Nov 14 2010