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A148293 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), (-1, 0, 1), (-1, 1, 0), (0, 0, 1), (1, 0, -1)} 1
1, 1, 2, 5, 13, 35, 109, 335, 1081, 3640, 12356, 43192, 153588, 552741, 2023770, 7484083, 27974294, 105662926, 402081552, 1543075131, 5962438750, 23183912562, 90707739797, 356731022840, 1410202516130, 5600482140935, 22336776813476, 89452688343270, 359555574826382, 1450365332698185, 5869680477211339 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..30.

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, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + 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: A149853 A148291 A148292 * A148294 A148295 A288540

Adjacent sequences:  A148290 A148291 A148292 * A148294 A148295 A148296

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 21 17:27 EDT 2019. Contains 323444 sequences. (Running on oeis4.)