A148158 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, 1), (0, -1, 1), (0, 1, 0), (1, 1, -1)}.

1, 1, 2, 4, 11, 30, 99, 321, 1125, 3994, 14669, 54883, 210009, 816899, 3221481, 12875307, 51984975, 211956185, 871637092, 3613651770, 15086421954, 63391684221, 267934026055, 1138417265769, 4860596083277, 20847396593292, 89793624085992, 388259714531135, 1684888139692659, 7336277575618726

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A135527 A215460 A339225 * A148159 A275310 A102814

Adjacent sequences: A148155 A148156 A148157 * A148159 A148160 A148161

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved