A151130 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), (0, 0, 1), (0, 1, 0), (1, 0, 1), (1, 1, -1)}

1, 3, 11, 45, 197, 889, 4101, 19231, 91215, 436473, 2102946, 10186704, 49561448, 241995991, 1185107619, 5818191754, 28623970526, 141074855063, 696366312010, 3441938435709, 17032200330398, 84367927756038, 418282312620433, 2075400048533778, 10304700885051731, 51196090539268890, 254493765468750694

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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + 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: A063024 A217887 A151129 * A216949 A074532 A049186

Adjacent sequences: A151127 A151128 A151129 * A151131 A151132 A151133

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved