A150037 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, 0, -1), (0, 0, 1), (0, 1, 1), (1, 0, -1)}.

1, 2, 6, 17, 64, 227, 871, 3349, 13604, 54859, 226053, 944291, 3996053, 16947058, 72706281, 314383547, 1365737918, 5956847932, 26165136183, 115396882757, 510350828873, 2266336213739, 10105247703118, 45164368781525, 202367655657864, 909643466845165, 4098711262737791, 18501421479978978

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, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + 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: A150035 A000661 A150036 * A150038 A150039 A150040

Adjacent sequences: A150034 A150035 A150036 * A150038 A150039 A150040

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved