A148796 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, 0), (0, 0, -1), (0, 1, 1), (1, -1, 0)}.

1, 1, 3, 8, 25, 83, 291, 1011, 3708, 13893, 52796, 201675, 786971, 3101031, 12312796, 49207116, 198635240, 806439581, 3290613339, 13498671882, 55687738095, 230635399029, 958715226219, 4001207405032, 16760299346945, 70409527378023, 296629186167545, 1253416038489361, 5310203644567979

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[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A148794 A143330 A148795 * A148797 A123638 A207651

Adjacent sequences: A148793 A148794 A148795 * A148797 A148798 A148799

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved