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A190360 Number of one-sided n-step prudent walks, avoiding 4 or more consecutive east steps. 2
1, 3, 7, 17, 40, 96, 229, 547, 1306, 3119, 7448, 17786, 42473, 101426, 242206, 578390, 1381200, 3298317, 7876408, 18808927, 44915872, 107259471, 256136497, 611656057, 1460639684, 3488019553, 8329419319, 19890721694, 47499206650 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n,k) is the number of one-sided n-step prudent walks, avoiding k or more consecutive east steps; k=4 in this sequence.

REFERENCES

S. Gao and H. Niederhausen, Sequences Arising From Prudent Self-Avoiding Walks, (submitted to INTEGERS: The Electronic Journal of Combinatorial Number Theory).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Shanzhen Gao, Keh-Hsun Chen, Tackling Sequences From Prudent Self-Avoiding Walks, FCS'14, The 2014 International Conference on Foundations of Computer Science.

FORMULA

G.f.: (1+t-t^k)/(1-2*t-t^2+t^(k+1)), (k=4 in this sequence).

MAPLE

b:= proc(n, i) option remember; `if`(n<0, 0,

      `if`(n=0, 1, b(n-1, 0) +`if`(i<=0, b(n-1, -1), 0)+

      `if`(i>=0 and i<3, b(n-1, i+1), 0)))

    end:

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

seq(a(n), n=0..30);  # Alois P. Heinz, Jun 04 2011

MATHEMATICA

(1+t-t^k)/(1-2*t-t^2+t^(k+1)) /. k -> 4 + O[t]^25 // CoefficientList[#, t]& (* Jean-Fran├žois Alcover, Oct 24 2016 *)

CROSSREFS

Cf. A006356 = a(n,2), A033303 = a(n,3).

Sequence in context: A036885 A247300 A137682 * A167213 A249753 A000600

Adjacent sequences:  A190357 A190358 A190359 * A190361 A190362 A190363

KEYWORD

nonn,walk

AUTHOR

Shanzhen Gao, May 09 2011

STATUS

approved

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Last modified July 17 14:39 EDT 2019. Contains 325106 sequences. (Running on oeis4.)