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A151128 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, 1), (0, 0, 1), (0, 1, 0), (1, 1, -1), (1, 1, 0)} 0
1, 3, 11, 45, 195, 875, 4019, 18769, 88737, 423485, 2035845, 9844041, 47823225, 233223195, 1141000497, 5597006081, 27517037763, 135543341549, 668754328733, 3304220895803, 16345726019499, 80947574798049, 401245717273397, 1990558979593701, 9882254070061675, 49092760257782911, 244021679144664917 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A151126 A151127 A026375 * A049183 A049166 A049172

Adjacent sequences:  A151125 A151126 A151127 * A151129 A151130 A151131

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified November 25 08:03 EST 2020. Contains 338618 sequences. (Running on oeis4.)