A148967 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), (-1, 0, 1), (0, 1, -1), (0, 1, 1), (1, -1, 0)}.

1, 1, 3, 9, 31, 108, 406, 1553, 6166, 24855, 102270, 425738, 1796144, 7649640, 32882918, 142419505, 621115219, 2724948992, 12019680168, 53274256405, 237154752119, 1059892552945, 4753922269447, 21392879707763, 96559640434061, 437046712139148, 1983228475255612, 9020883495444314, 41122820816912023

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A148966 A279971 A127927 * A189429 A123222 A148968

Adjacent sequences: A148964 A148965 A148966 * A148968 A148969 A148970

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved