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A191653 Number of n-step two-sided prudent self-avoiding walks ending at the northwest corner of their box. 2
1, 2, 4, 9, 20, 46, 105, 244, 567, 1328, 3114, 7334, 17301, 40925, 96955, 230128, 546942, 1301721, 3101513, 7397751, 17661413, 42201765, 100918554, 241504437, 578312697, 1385684687, 3322065246, 7968514308, 19122960036, 45912141148, 110276058832, 264974818317 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

M. Bousquet-Mélou, Families of prudent self-avoiding walks, DMTCS proc. AJ, 2008, 167-180.

E. Duchi, On some classes of prudent walks, in: FPSAC'05, Taormina, Italy, 2005.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..700

EXAMPLE

a(4) = 20: ENNW, ENWN, ENWW, NENW, NNNN, NNNW, NNWN, NNWW, NWNN, NWNW, NWWN, NWWW, WNNN, WNNW, WNWN, WNWW, WWNN, WWNW, WWWN, WWWW.

MAPLE

b:= proc(d, i, n, x, y, w) option remember;

      `if`(y+w>n, 0, `if`(n=0, `if`(y=0 and w=0, 1, 0),

         `if`(d<>3, b(1, evalb(x=0), n-1, max(x-1, 0), y, w+1), 0) +

         `if`(d<>4, b(2, evalb(y=0), n-1, x, max(y-1, 0), w), 0) +

         `if`(d in [0, 3] or d=2 and i, b(3, false, n-1, x+1, y,

              max(w-1, 0)), 0) +

         `if`(d in [0, 4] or d=1 and i, b(4, false, n-1, x, y+1, w), 0)))

    end:

a:= n-> b(0, false, n, 0, 0, 0):

seq(a(n), n=0..30);

CROSSREFS

Cf. A191605, A191625, A191652.

Sequence in context: A036617 A007902 A057417 * A191827 A000968 A005908

Adjacent sequences:  A191650 A191651 A191652 * A191654 A191655 A191656

KEYWORD

nonn,walk

AUTHOR

Alois P. Heinz, Jun 10 2011

STATUS

approved

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Last modified February 25 14:46 EST 2018. Contains 299654 sequences. (Running on oeis4.)