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A150119 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), (1, 1, 0)} 0
1, 2, 6, 19, 72, 278, 1151, 4785, 20830, 90633, 406619, 1820791, 8341056, 38108083, 177174571, 821368540, 3861043640, 18098240838, 85798070413, 405641837783, 1935882725587, 9215475026569, 44216454807026, 211658838000237, 1020022720191234, 4905155570746317, 23725240033392488, 114529446530119485 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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[-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: A038392 A044045 A150118 * A268569 A181770 A138800

Adjacent sequences:  A150116 A150117 A150118 * A150120 A150121 A150122

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified October 21 03:24 EDT 2019. Contains 328291 sequences. (Running on oeis4.)