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A148148 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, 1, -1), (0, 0, 1), (0, 1, -1), (1, -1, 1)} 0
1, 1, 2, 4, 11, 29, 96, 298, 1054, 3583, 13186, 47814, 181866, 689996, 2694846, 10555991, 42124128, 168981868, 686507904, 2805640764, 11570860322, 47999433566, 200491056182, 841954166578, 3555238501487, 15084229335206, 64293966708470, 275188404585194, 1182506179100655, 5099853474975899 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..29.

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148146 A148147 A298269 * A148149 A034769 A219017

Adjacent sequences:  A148145 A148146 A148147 * A148149 A148150 A148151

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified August 15 01:56 EDT 2020. Contains 336485 sequences. (Running on oeis4.)