A148624 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, 0, -1), (0, 1, -1), (1, 0, 1)}.

1, 1, 3, 6, 22, 54, 212, 601, 2419, 7359, 30707, 98305, 415115, 1386984, 5944884, 20395903, 88370175, 311007253, 1357288223, 4866804666, 21404173960, 77985019982, 344771120040, 1273702029750, 5659467047244, 21147247235020, 94361020337860, 356237054150967, 1595259005678097, 6075789783955394

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A054297 A325158 A079514 * A148625 A148626 A148627

Adjacent sequences: A148621 A148622 A148623 * A148625 A148626 A148627

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved