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A149915 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), (-1, 1, -1), (0, 0, 1), (1, 0, 0)}. 0
1, 2, 5, 15, 47, 155, 535, 1903, 6939, 25811, 97548, 373748, 1448881, 5673375, 22408892, 89180910, 357297116, 1440071723, 5835251538, 23758746695, 97156064567, 398866291815, 1643428912223, 6793754985019, 28170107399019, 117134098136219, 488318466886486, 2040648616229122, 8546860834956835 (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, k, -1 + n] + aux[i, j, -1 + k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
CROSSREFS
Sequence in context: A364161 A148364 A172405 * A149916 A149917 A149918
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified April 25 11:39 EDT 2024. Contains 371969 sequences. (Running on oeis4.)