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A148823 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, 0), (1, 0, 1), (1, 1, -1)}. 0
1, 1, 3, 8, 27, 79, 291, 958, 3536, 11919, 45346, 159573, 608185, 2165579, 8367723, 30441954, 117663978, 430907544, 1678947661, 6228642012, 24271972371, 90437139766, 354216216105, 1331129719318, 5213476692361, 19651150753314, 77237939630180, 292909168969304, 1151199696089107, 4375450153625250 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A347830 A305049 A332833 * A205503 A242537 A323795
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified August 30 21:20 EDT 2024. Contains 375548 sequences. (Running on oeis4.)