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A149894 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, 0), (0, 0, 1), (0, 1, 0), (1, 0, -1)}. 0
1, 2, 5, 14, 45, 155, 558, 2080, 7981, 31333, 125347, 509443, 2097949, 8739652, 36773651, 156084172, 667620841, 2875253212, 12459142364, 54287523254, 237728626706, 1045768644168, 4619449301099, 20483062314916, 91141603965834, 406853466552560, 1821606848244420, 8178490232193612 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A149891 A149892 A149893 * A030126 A081444 A268004
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified May 7 11:03 EDT 2024. Contains 372302 sequences. (Running on oeis4.)