A150549 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, 0, 0), (0, 0, 1), (1, -1, 0), (1, 0, -1), (1, 1, 0)}.

1, 2, 7, 26, 105, 438, 1883, 8261, 36829, 166217, 757759, 3482883, 16118980, 75034272, 351040611, 1649438104, 7779730832, 36817013598, 174754037184, 831695343920, 3967751325946, 18970059631721, 90876481086451, 436132617878930, 2096548639639431, 10093770798999128, 48664640611491510, 234930979186383682

Offset

0,2

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A141370 A150547 A150548 * A150550 A150551 A150552

Adjacent sequences: A150546 A150547 A150548 * A150550 A150551 A150552

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved