A150013 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, 1), (0, 1, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 5, 17, 65, 237, 967, 3984, 16160, 68745, 296712, 1262510, 5540252, 24489806, 107196022, 478859777, 2150448033, 9584178330, 43349477053, 196821411031, 888311338529, 4054202839269, 18556916269822, 84530021363135, 388430674507119, 1788984148930394, 8206817078963654, 37913828922747116

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A217596 A090902 A150012 * A052539 A123166 A008932

Adjacent sequences: A150010 A150011 A150012 * A150014 A150015 A150016

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved