A077482 Number of self-avoiding walks on square lattice trapped after n steps.

1, 2, 11, 25, 95, 228, 752, 1860, 5741, 14477, 42939, 109758, 317147, 818229, 2322512, 6030293, 16900541, 44079555, 122379267, 320227677, 882687730, 2315257359, 6346076015, 16675422679, 45502168379, 119728011251, 325510252108, 857400725204

Offset

7,2

Comments

Only 1/8 of all possible walks is counted by selecting the first step in +x direction and requiring the first step changing y to be positive.

References

See references given for A001411.

Links

Table of n, a(n) for n=7..34.

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

Eric Weisstein's World of Mathematics, Self-Avoiding Walk.

Example

a(7) = 1 because there is only 1 self-trapping walk with 7 steps: (0,0)(1,0)(1,1)(1,2)(0,2)(-1,2)(-1,1)(0,1); a(8) = 2 because there are 2 self-trapping walks with 8 steps: (0,0)(1,0)(2,0)(2,1)(2,2)(1,2)(0,2)(0,1)(1,1) and (0,0)(1,0)(1,1)(2,1)(3,1)(3,0)(3,-1)(2,-1)(2,0).

Prog

(Fortran) c Program provided at given link.

Crossrefs

Cf. A001411, A046661, A174517, A322831.

Sequence in context: A084547 A241238 A296285 * A141428 A371344 A104085

Adjacent sequences: A077479 A077480 A077481 * A077483 A077484 A077485

Keyword

more,nonn,walk,changed

Author

Hugo Pfoertner, Nov 07 2002

Extensions

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

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

Status

approved