A149521 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, 0), (-1, 1, -1), (1, -1, 0), (1, 1, 1)}

1, 1, 5, 11, 51, 147, 691, 2229, 10569, 36587, 174151, 631267, 3015819, 11297343, 54109527, 207809319, 997352927, 3905712813, 18775928973, 74694466147, 359566404155, 1449137185583, 6983876576051, 28456062978505, 137272752795641, 564570822135359, 2725789916924483, 11301486545827607

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, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A073415 A176832 A289284 * A149522 A149523 A149524

Adjacent sequences: A149518 A149519 A149520 * A149522 A149523 A149524

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved