A149905 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, -1), (1, -1, 1), (1, 0, 0), (1, 0, 1)}.

1, 2, 5, 14, 48, 166, 613, 2280, 8976, 35247, 143382, 582249, 2431920, 10125351, 43070020, 182684943, 788474211, 3393379082, 14813919095, 64502077124, 284229195699, 1249444788695, 5548487320409, 24585551900503, 109894795683645, 490239938536434, 2203608385587727, 9887231443885407

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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A143918 A129867 A119841 * A149906 A129778 A060797

Adjacent sequences: A149902 A149903 A149904 * A149906 A149907 A149908

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved