A151022 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, 0), (-1, 1, 0), (1, -1, 0), (1, 1, 0), (1, 1, 1)}.

1, 2, 10, 36, 180, 752, 3760, 16736, 83680, 385344, 1926720, 9058512, 45292560, 215891600, 1079458000, 5195196624, 25975983120, 125901336112, 629506680560, 3067403607504, 15337018037520, 75041661844720, 375208309223600, 1841832138224720, 9209160691123600, 45324878456036464, 226624392280182320

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A256105 A151020 A151021 * A144895 A236767 A154323

Adjacent sequences: A151019 A151020 A151021 * A151023 A151024 A151025

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved