A150878 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, -1, 1), (0, 1, 0), (1, 1, -1), (1, 1, 1)}.

1, 2, 8, 33, 148, 678, 3170, 15031, 72005, 347380, 1686183, 8220575, 40224283, 197408025, 971135812, 4787131799, 23637741484, 116884315128, 578682102065, 2868005586752, 14227054930667, 70630844476456, 350892598875605, 1744288604393072, 8675524001624688, 43169753022104862, 214905305285321910

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, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + 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: A150875 A150876 A150877 * A150879 A150880 A150881

Adjacent sequences: A150875 A150876 A150877 * A150879 A150880 A150881

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved