

A122951


Number of walks from (0,0) to (n,n) in the region x >= y with the steps (1,0), (0,1), (2,0) and (0,2).


8



1, 1, 5, 22, 117, 654, 3843, 23323, 145172, 921508, 5942737, 38825546, 256431172, 1709356836, 11485249995, 77703736926, 528893901963, 3619228605738, 24884558358426, 171828674445330, 1191050708958096, 8284698825305832
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OFFSET

0,3


COMMENTS

When this walk is further restricted to the subset of the plane xy <= 2, this gives the sequence A046717. Similarly, the sequence for such a walk restricted to xy <= w (w > 2) is not present in the OEIS. The reference provided proves recurrences for generating functions in w.


LINKS



FORMULA

In Maple, GF is given by solve(z^4*F^4 2*z^3*F^3 z^2*F^3 +2*z^2*F^2 +3*z*F^2 2*z*FF+1, F);


EXAMPLE

a(2 = 5 because we can reach (2,2) in the following ways:
(0,0),(1,0),(1,1),(2,1),(2,2)
(0,0),(2,0),(2,2)
(0,0),(1,0),(2,0),(2,2)
(0,0),(2,0),(2,1),(2,2)
(0,0),(1,0),(2,0),(2,1),(2,2).


MAPLE

N:= 100: # to get a[0] to a[N]
S:= series(RootOf(z^4*F^42*z^3*F^3z^2*F^3+2*z^2*F^2+3*z*F^22*z*FF+1, F), z, N+1):


MATHEMATICA

f[x_] = (2x+Sqrt[4(x2)x+1]  Sqrt[2]Sqrt[2x(2x + Sqrt[4(x2)x+1]1) + Sqrt[4(x2)x+1]+1]+1)/(4x^2);
CoefficientList[Series[f[x], {x, 0, 21}], x]


CROSSREFS



KEYWORD

nonn,nice,walk


AUTHOR



STATUS

approved



