

A046661


Number of nstep selfavoiding walks on the square lattice with first step specified.


8



1, 3, 9, 25, 71, 195, 543, 1479, 4067, 11025, 30073, 81233, 220375, 593611, 1604149, 4311333, 11616669, 31164683, 83779155, 224424291, 602201507, 1611140121, 4316653453, 11536599329, 30870338727, 82428196555, 220329372907
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OFFSET

1,2


COMMENTS

Used as the denominator for the mean square displacement of all different selfavoiding nstep walks in A078797.  Hugo Pfoertner, Dec 09 2002
Number of ways a toy snake with n segments can be bent without flipping the snake upside down. Each segment must perpendicular or parallel with each adjacent segment. A "slither" is a way of writing down the configuration of a snake; starting from the tail, write down which direction the next segment is pointing (R for right, S for straight, L for left). E.g., a snake with 10 segments may have the valid slither RLRRLLRRL, but not RSRRSSLSL.


REFERENCES

a(n) = A001411(n)/4 = A002900(n)/2.


LINKS

Hugo Pfoertner, Table of n, a(n) for n = 1..79
G. T. Barkema and S. Flesia, Twodimensional oriented selfavoiding walks with parallel contacts, J. Stat. Phys. 85 (1996) no 3/4, 363381 [a(30) to a(34)]
D. BennetWood, J. L. Cardy, S. Flesia, A. J. Guttmann et al., Oriented selfavoiding walks with orientationdependent interactions, J. Phys. A: Math. Gen. 28 (1995) no 18, 51435163, [up to a(29)]
V. Hart, How to Snakes, Video (2011)


MATHEMATICA

(* b = A001411 *) mo = Tuples[{1, 1}, 2]; b[0] = 1; b[tg_, p_:{{0, 0}}] := b[tg, p] = Block[{e, mv = Complement[Last[p] + #& /@ mo, p]}, If[tg == 1, Length[mv], Sum[b[tg  1, Append[p, e]], {e, mv}]]];
a[n_] := b[n]/4;
Table[an = a[n]; Print[an]; an, {n, 1, 16}] (* JeanFrançois Alcover, Nov 02 2018, after Giovanni Resta in A001411 *)


CROSSREFS

Cf. A001411, A002900, A078797.
Sequence in context: A211284 A211283 A058719 * A309105 A101197 A233828
Adjacent sequences: A046658 A046659 A046660 * A046662 A046663 A046664


KEYWORD

nonn,walk


AUTHOR

N. J. A. Sloane


STATUS

approved



