A150843 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, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 8, 32, 138, 616, 2816, 13108, 61764, 293968, 1409604, 6800654, 32970232, 160487760, 783813576, 3838839984, 18845981576, 92707895520, 456847371156, 2254651625402, 11141837104710, 55122849299652, 272988026623936, 1353135158061896, 6712438835266828, 33321394925379744, 165514812006856556

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A150842 A274483 A308152 * A150844 A141380 A151304

Adjacent sequences: A150840 A150841 A150842 * A150844 A150845 A150846

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved