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A190528 Number of n-step one-sided prudent walks avoiding exactly three consecutive West steps. 1
1, 3, 7, 16, 39, 92, 219, 521, 1238, 2944, 6999, 16640, 39562, 94058, 223623, 531663, 1264027, 3005221, 7144904, 16986989, 40386518, 96018831, 228284497, 542745740, 1290376448, 3067866323, 7293843428, 17341091936, 41228396592, 98020395245 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (2, 1, 0, -1, 1).

FORMULA

G.f.: x*(1+x-x^3+x^4)/(1-2*x-x^2+x^4-x^5).

a(0)=1, a(1)=3, a(2)=7, a(3)=16, a(4)=39, a(n)=2*a(n-1)+a(n-2)- a(n-4)+ a(n-5) [From Harvey P. Dale, Sep 20 2011]

EXAMPLE

a(3)=16 since there are 16 such walks: WWN, NWW, WNN, WNW, WNE, NNN, NNW, NNE, NEE, NWN, NEN, EEE, EEN, ENW, ENN, ENE.

MATHEMATICA

Rest[CoefficientList[Series[x (1+x-x^3+x^4)/(1-2x-x^2+x^4-x^5), {x, 0, 40}], x]] (* or *) LinearRecurrence[{2, 1, 0, -1, 1}, {1, 3, 7, 16, 39}, 40] (* Harvey P. Dale, Sep 20 2011 *)

PROG

(PARI) Vec(x*(1+x-x^3+x^4)/(1-2*x-x^2+x^4-x^5)+O(x^66)) [Joerg Arndt, May 13 2011]

CROSSREFS

Sequence in context: A196154 A227235 A152090 * A203611 A176604 A014140

Adjacent sequences:  A190525 A190526 A190527 * A190529 A190530 A190531

KEYWORD

nonn,walk

AUTHOR

Shanzhen Gao, May 11 2011

STATUS

approved

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Last modified February 22 13:55 EST 2018. Contains 299454 sequences. (Running on oeis4.)