A150517 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, 1), (0, -1, 1), (0, 1, 0), (0, 1, 1), (1, 1, -1)}.

1, 2, 7, 25, 103, 430, 1888, 8408, 38226, 175815, 817224, 3829788, 18066154, 85701157, 408415216, 1954027018, 9380461812, 45162925477, 217995988510, 1054592233454, 5111892519740, 24822411459013, 120723483917760, 587971858333280, 2867338818710023, 13999361611617617, 68422574023951818

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150514 A150515 A150516 * A150518 A150519 A150520

Adjacent sequences: A150514 A150515 A150516 * A150518 A150519 A150520

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved