A151074 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, 0), (0, 1, -1), (0, 1, 0), (1, 0, 0), (1, 0, 1)}.

1, 3, 10, 40, 169, 723, 3214, 14570, 66467, 307797, 1438868, 6752762, 31934236, 151832097, 723820039, 3466177340, 16655030010, 80181728016, 387141121436, 1873550930655, 9080050327816, 44094481742754, 214485799818078, 1044473982743553, 5093661578986069, 24871301698286623, 121549003554477777

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A089005 A287887 A088300 * A151075 A151076 A151077

Adjacent sequences: A151071 A151072 A151073 * A151075 A151076 A151077

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved