A078528 Number of unconstrained walks on square lattice trapped after n steps.

1, 1, 2, 5, 15, 30, 76, 170, 422, 961, 2339, 5390, 12977, 30059, 71918, 167019, 397691, 924931, 2194478, 5107991, 12085695, 28143758, 66442935, 154759821, 364706675, 849562628

Offset

7,3

Comments

See under A078527. In the probability sum in A077483 and A078526 the unconstrained walks are responsible for the occurrence of 3^(n-1) in the denominator of P(n).

Links

Table of n, a(n) for n=7..32.

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

Example

a(7)=1 because the unique shortest walk contains no constrained steps. a(10)=5: See illustration in "5 Unconstrained and 7 maximally 2-constrained walks of length 10" given at link.

Prog

(Fortran) c Program provided at given link

Crossrefs

Cf. A077482, A077483, A078526, A078527, A001411.

Sequence in context: A290836 A396906 A191313 * A309272 A393937 A077686

Adjacent sequences: A078525 A078526 A078527 * A078529 A078530 A078531

Keyword

more,nonn

Author

Hugo Pfoertner, Nov 27 2002

Extensions

a(24)-a(32) from Sean A. Irvine, Jul 03 2025

Status

approved