A150631 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), (0, -1, 1), (0, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 27, 115, 501, 2266, 10414, 48673, 229899, 1095774, 5259354, 25385793, 123107126, 599282303, 2926781377, 14332693879, 70352155139, 346012928712, 1704732039933, 8411438735489, 41557786740897, 205557391371019, 1017777949837131, 5043845141082382, 25015871533786025, 124158696941193602

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[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + 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: A154108 A150629 A150630 * A150632 A150633 A150634

Adjacent sequences: A150628 A150629 A150630 * A150632 A150633 A150634

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved