A149354 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, 0, 0), (-1, 1, 1), (0, -1, 0), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 12, 42, 158, 619, 2456, 10094, 42190, 178778, 767298, 3334324, 14614763, 64576389, 287507718, 1288326564, 5805041546, 26294197307, 119665532949, 546883448861, 2508962305902, 11551838992820, 53360922039204, 247227762954157, 1148650754773288, 5350668191881004, 24984699902169147

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149351 A149352 A149353 * A197659 A360468 A292287

Adjacent sequences: A149351 A149352 A149353 * A149355 A149356 A149357

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved