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A151284 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 1), (0, 1), (1, -1), (1, 0)} 0
1, 2, 6, 20, 70, 254, 942, 3550, 13532, 52030, 201386, 783560, 3061442, 12001804, 47181278, 185904220, 733908634, 2901998092, 11490757796, 45552262860, 180762964146, 717939220774, 2853611232902, 11349816190552, 45168339253888, 179845805435900, 716409551285034, 2854926106932244 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..27.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

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[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

CROSSREFS

Sequence in context: A000984 A087433 A119373 * A049138 A095929 A078482

Adjacent sequences:  A151281 A151282 A151283 * A151285 A151286 A151287

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified February 17 18:30 EST 2018. Contains 299296 sequences. (Running on oeis4.)