7,2

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.

See references given for A001411

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

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

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) (0,0)(1,0)(1,1)(2,1)(3,1)(3,0)(3,-1)(2,-1)(2,0)

FORTRAN program provided at given link.

Cf. A046661, A001411.

Sequence in context: A009189 A012213 A012251 this_sequence A141428 A104085 A080663

Adjacent sequences: A077479 A077480 A077481 this_sequence A077483 A077484 A077485

more,nonn,walk

Hugo Pfoertner (hugo(AT)pfoertner.org), Nov 07 2002