A148657 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, 1), (-1, 0, 1), (1, -1, -1), (1, 1, 0)}

1, 1, 3, 6, 25, 65, 254, 789, 3276, 10614, 44813, 155906, 661434, 2362970, 10220577, 37614941, 162469168, 612478229, 2669883881, 10204917780, 44610693636, 173498753593, 760158224730, 2986524969699, 13137421409875, 52170082765338, 229643658222326, 920137704825030, 4060516913281992

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, -1 + j, 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] + 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: A288760 A144227 A174473 * A148658 A148659 A148660

Adjacent sequences: A148654 A148655 A148656 * A148658 A148659 A148660

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved