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A151065 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, 0, -1), (0, 0, 1), (1, 0, 0), (1, 1, 0)}. 0
1, 3, 10, 39, 156, 651, 2803, 12218, 54331, 244094, 1106978, 5068058, 23334902, 108150502, 503753548, 2356387859, 11069504275, 52169455719, 246667514552, 1169587215167, 5559341257547, 26488381338623, 126466805257309, 604986670813445, 2899284252998229, 13916709926795557, 66904010992079948 (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, -1 + j, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 1 + 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: A300974 A149051 A151064 * A151066 A151067 A007163
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified June 21 21:50 EDT 2024. Contains 373559 sequences. (Running on oeis4.)