A148742 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, 0, 1), (-1, 1, 1), (1, 0, -1), (1, 0, 0)}.

1, 1, 3, 7, 27, 74, 311, 973, 4225, 14281, 63741, 226243, 1028848, 3789405, 17450224, 66115864, 307457417, 1190882793, 5580880556, 22007193489, 103768034736, 415307788212, 1968152808212, 7975987369231, 37958127803864, 155474827122061, 742557291607324, 3069658849260929, 14705810083112145

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A056257 A066021 A259595 * A148743 A148744 A148745

Adjacent sequences: A148739 A148740 A148741 * A148743 A148744 A148745

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved