A174517 Partial sums of A077482.

1, 3, 14, 39, 134, 362, 1114, 2974, 8715, 23192, 66131, 175889, 493036, 1311265, 3633777, 9664070, 26564611, 70644166, 193023433, 513251110, 1395938840, 3711196199, 10057272214, 26732694893, 72234863272, 191962874523, 517473126631, 1374873851835

Offset: 7

Author

Jonathan Vos Post, Mar 21 2010

Keywords

• more
• nonn

Comments

Partial sums of number of self-avoiding walks on square lattice trapped after n steps.

A self-trapping walk is a walk which ends when the walker is "trapped" or surrounded by previously visited sites on the lattice.

Examples

			a(16) = 1 + 2 + 11 + 25 + 95 + 228 + 752 + 1860 + 5741 + 14477 = 23192.
		

References

• B. D. Hughes, Random Walks and Random Environments, Vol. I OUP, 1995.
• N. Madras & G. Slade, The Self-Avoiding Walk, Birkhäuser, 1993.

Links

• Hugo Pfoertner, Results for the 2D Self-Trapping Random Walk.

Crossrefs

Cf. A077482, A046661, A001411, A322831.

Formula

a(n) = Sum_{i=7..n} A077482(i).

Extensions

a(26)-a(28) from Alois P. Heinz, Jun 16 2011

a(29)-a(34) from Bert Dobbelaere, Jan 03 2019