A148156 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, 0, 1), (0, -1, 1), (0, 1, 0), (1, 0, -1)}.

1, 1, 2, 4, 11, 30, 96, 298, 1028, 3485, 12724, 45705, 173541, 650298, 2544692, 9844616, 39436571, 156427321, 638580481, 2584305014, 10714655777, 44081695845, 185148725201, 772276053413, 3279498523275, 13839450883147, 59326871290544, 252873214965116, 1092926867474669, 4698994759995838

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, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148154 A148155 A007719 * A148157 A141268 A135527

Adjacent sequences: A148153 A148154 A148155 * A148157 A148158 A148159

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved