A149719 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, 1, 0), (0, 1, -1), (1, -1, 0), (1, 1, 1)}.

1, 1, 5, 17, 73, 293, 1321, 5683, 26401, 118077, 557041, 2552623, 12165169, 56663723, 272055017, 1282219173, 6190286979, 29434445015, 142709451071, 683201772937, 3323631867519, 15996936093245, 78034908308989, 377215215035773, 1844258407626715, 8946650765197433, 43824287063348705, 213222556417381955

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[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A084777 A149717 A149718 * A149720 A149721 A325156

Adjacent sequences: A149716 A149717 A149718 * A149720 A149721 A149722

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved