A148789 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, 0), (0, 1, 1), (1, 1, -1)}.

1, 1, 3, 8, 25, 77, 252, 848, 2894, 10064, 35290, 125487, 450179, 1626087, 5916476, 21633851, 79579418, 294022842, 1090624361, 4061006824, 15168490711, 56843270546, 213593833242, 804616157278, 3038263114399, 11496594775537, 43593624433215, 165604694730541, 630191189599674, 2402056664402975

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, 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: A292778 A022553 A292884 * A088327 A148790 A148791

Adjacent sequences: A148786 A148787 A148788 * A148790 A148791 A148792

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved