A148750 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), (1, -1, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 3, 7, 27, 91, 401, 1601, 7423, 32011, 151937, 683445, 3289407, 15195887, 73826601, 347300701, 1698509579, 8094184535, 39775700609, 191355999417, 943683591813, 4572456580749, 22609674781031, 110153525765667, 545799821299537, 2670545688893781, 13253449653142241, 65069191500414525

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, j, k, -1 + n] + aux[-1 + i, 1 + j, -1 + 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: A148748 A148749 A098465 * A081562 A216174 A260464

Adjacent sequences: A148747 A148748 A148749 * A148751 A148752 A148753

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved