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A148055 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, 1, -1), (-1, 1, 1), (1, 0, 0)} 0
1, 1, 2, 3, 10, 20, 68, 147, 558, 1308, 4840, 11638, 45142, 112918, 431806, 1095775, 4299562, 11168048, 43431360, 113876158, 449752342, 1197311782, 4700292130, 12596627212, 49945553674, 135283990390, 534123243068, 1454033588472, 5779639647718, 15857393541418, 62837646837160, 173088744641491 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..31.

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, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148052 A148053 A148054 * A089791 A297872 A298135

Adjacent sequences:  A148052 A148053 A148054 * A148056 A148057 A148058

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified July 25 02:57 EDT 2021. Contains 346282 sequences. (Running on oeis4.)