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A149189 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, -1, 0), (-1, 0, -1), (-1, 1, 1), (0, -1, 1), (1, 1, 0)} 0
1, 1, 4, 10, 37, 126, 472, 1765, 6878, 26812, 107028, 428929, 1740321, 7098405, 29176482, 120454790, 500030927, 2083449191, 8715752041, 36576288141, 153968912861, 649844829206, 2749607363057, 11659719519993, 49545446311575, 210926363580093, 899529315714847, 3842334024093159 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

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, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A154152 A025237 A149188 * A149190 A102755 A197551

Adjacent sequences:  A149186 A149187 A149188 * A149190 A149191 A149192

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified February 19 21:04 EST 2019. Contains 320328 sequences. (Running on oeis4.)