A148797 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), (0, 1, -1), (1, 0, 1)}.

1, 1, 3, 8, 25, 83, 298, 998, 3889, 13971, 54308, 206572, 814236, 3160726, 12741671, 50085798, 204433734, 817602541, 3353224962, 13598332084, 56149216881, 229527402171, 954687076546, 3929609745078, 16422590530819, 68079724229740, 285531311235577, 1190403796535917, 5011656233673621

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, -1 + k, -1 + n] + aux[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: A143330 A148795 A148796 * A123638 A207651 A361959

Adjacent sequences: A148794 A148795 A148796 * A148798 A148799 A148800

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved