login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A046661 Number of n-step self-avoiding 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Used as the denominator for the mean square displacement of all different self-avoiding n-step 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, Two-dimensional oriented self-avoiding walks with parallel contacts, J. Stat. Phys. 85 (1996) no 3/4, 363-381 [a(30) to a(34)]

D. Bennet-Wood, J. L. Cardy, S. Flesia, A. J. Guttmann et al., Oriented self-avoiding walks with orientation-dependent interactions, J. Phys. A: Math. Gen. 28 (1995) no 18, 5143-5163, [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}] (* Jean-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 17:36 EST 2019. Contains 329865 sequences. (Running on oeis4.)