A150739 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), (1, 0, -1), (1, 1, 1)}

1, 2, 8, 29, 122, 516, 2275, 10063, 45677, 208078, 959078, 4449565, 20770805, 97420555, 459170757, 2171832581, 10307926187, 49070391239, 234218338080, 1120565600586, 5372827196955, 25811427398839, 124218131253080, 598779633094643, 2890670050736226, 13974041594587039, 67639306569008879

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, -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: A150736 A150737 A150738 * A151301 A150740 A150741

Adjacent sequences: A150736 A150737 A150738 * A150740 A150741 A150742

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved