A148321 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, 1), (-1, 1, 0), (0, -1, 1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 5, 14, 40, 127, 418, 1424, 5031, 18209, 67366, 254186, 974761, 3791854, 14943935, 59552233, 239744109, 974027603, 3989625078, 16464722934, 68411771010, 286027517137, 1202755713725, 5084367828630, 21598046004481, 92163416534879, 394937069941730, 1699022185812757, 7336018013119783

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, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A076866 A151417 A045632 * A007463 A159308 A163189

Adjacent sequences: A148318 A148319 A148320 * A148322 A148323 A148324

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved