A149984 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), (-1, 1, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 5, 17, 55, 200, 737, 2800, 10875, 42686, 170295, 683805, 2774827, 11322576, 46519469, 192043347, 796633305, 3317740288, 13867861969, 58155460455, 244585944419, 1031416896354, 4359870977953, 18470484019178, 78406877383159, 333459678106346, 1420613236435519, 6061821842982527

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A149981 A149982 A149983 * A149985 A149986 A121193

Adjacent sequences: A149981 A149982 A149983 * A149985 A149986 A149987

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved