A151071 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), (1, 0, 0), (1, 1, 0)}.

1, 3, 10, 39, 161, 688, 3030, 13679, 62583, 289432, 1352823, 6371322, 30171367, 143636119, 686989470, 3297242248, 15873914485, 76644248698, 370959805872, 1799101070446, 8742006194463, 42551408510633, 207421894977486, 1012449506176614, 4948029015857372, 24208750550937740, 118561279931909506

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, k, -1 + n] + aux[-1 + i, j, 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: A151068 A151069 A151070 * A063022 A371713 A218001

Adjacent sequences: A151068 A151069 A151070 * A151072 A151073 A151074

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved