

A151348


Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(1, 1), (1, 0), (1, 1), (0, 1), (1, 0)}


0



1, 0, 1, 1, 4, 7, 25, 64, 201, 612, 1961, 6355, 21026, 70968, 241810, 837191, 2925393, 10334302, 36813216, 132242756, 478470272, 1742816732, 6387201912, 23539830561, 87207544029, 324627673245, 1213820275167, 4557447698656, 17177881979810, 64981216839823, 246648317043660, 939184339480746, 3586940782960596
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OFFSET

0,5


LINKS

Table of n, a(n) for n=0..32.
A. Bostan, K. Raschel, B. Salvy, NonDfinite excursions in the quarter plane, J. Comb. Theory A 121 (2014) 4563, Table 1 Tag 21, Tag 33.
M. BousquetMélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.


MATHEMATICA

aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0  Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[1 + i, j, 1 + n] + aux[i, 1 + j, 1 + n] + aux[1 + i, 1 + j, 1 + n] + aux[1 + i, j, 1 + n] + aux[1 + i, 1 + j, 1 + n]]; Table[aux[0, 0, n], {n, 0, 25}]


CROSSREFS

Sequence in context: A073218 A276288 A219700 * A211942 A110413 A075686
Adjacent sequences: A151345 A151346 A151347 * A151349 A151350 A151351


KEYWORD

nonn,walk


AUTHOR

Manuel Kauers, Nov 18 2008


STATUS

approved



