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A150089 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, 0, 0), (0, 1, 0), (1, 0, -1), (1, 1, 0)}. 0
1, 2, 6, 19, 66, 243, 930, 3677, 14893, 61580, 258798, 1103083, 4757383, 20729422, 91130929, 403776628, 1801448724, 8086934285, 36504894978, 165610128497, 754727631760, 3453706751619, 15864249216608, 73123710278400, 338129830741337, 1568159784767825, 7292647519656839, 34000453643498153 (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, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A150086 A150087 A150088 * A150090 A150091 A190737
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified July 25 06:59 EDT 2024. Contains 374586 sequences. (Running on oeis4.)