A149611 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, -1, 1), (0, 1, -1), (1, 1, 1)}

1, 1, 5, 15, 63, 239, 1011, 4189, 18057, 77893, 341857, 1507917, 6713433, 30039549, 135215513, 611198839, 2774510515, 12637593187, 57749756479, 264625723379, 1215708590859, 5597697967779, 25828427689907, 119400088500319, 552925785793747, 2564597556922403, 11912703626624975, 55410318800011595

Offset

0,3

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, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[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: A149608 A149609 A149610 * A149612 A149613 A149614

Adjacent sequences: A149608 A149609 A149610 * A149612 A149613 A149614

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved