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A148736 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (-1, 1, 1), (0, -1, 0), (1, 0, 0), (1, 1, -1)} 0
1, 1, 3, 7, 25, 84, 321, 1227, 4914, 19934, 82989, 349811, 1498388, 6484077, 28361043, 125070229, 555952836, 2487523158, 11199379630, 50690294588, 230576659493, 1053425813447, 4832430453496, 22249194991314, 102789249165569, 476349608483292, 2213934802216253, 10317088128287144, 48198495684655758 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

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

MATHEMATICA

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A118398 A047974 A148735 * A148737 A148738 A148739

Adjacent sequences:  A148733 A148734 A148735 * A148737 A148738 A148739

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified January 21 22:47 EST 2020. Contains 331129 sequences. (Running on oeis4.)