A150744 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, -1), (-1, -1, 1), (0, 1, -1), (1, 0, 1), (1, 1, 1)}

1, 2, 8, 29, 125, 522, 2368, 10369, 48427, 218353, 1033431, 4763553, 22711231, 106299072, 509809530, 2410736596, 11620607296, 55359720508, 267922804476, 1283881994116, 6232712214286, 30010216869963, 146049623795791, 705957730100002, 3442921629724988, 16694925892971832, 81568648137262758

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, 1 + 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: A150741 A150742 A150743 * A150745 A150746 A150747

Adjacent sequences: A150741 A150742 A150743 * A150745 A150746 A150747

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved