

A077482


Number of selfavoiding walks on square lattice trapped after n steps.


13



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
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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 SelfTrapping Random Walk
Eric Weisstein's World of Mathematics, SelfAvoiding Walk.


EXAMPLE

a(7) = 1 because there is only 1 selftrapping 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 selftrapping 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 program provided at given link.


CROSSREFS

Cf. A001411, A046661, A174517, A322831.
Sequence in context: A012251 A241238 A296285 * A141428 A104085 A080663
Adjacent sequences: A077479 A077480 A077481 * A077483 A077484 A077485


KEYWORD

more,nonn,walk


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



