A149643 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, 0, 0), (-1, 0, 1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 15, 71, 243, 1173, 4425, 21623, 85595, 420601, 1718067, 8475957, 35414065, 175191261, 744299953, 3688985463, 15875795231, 78795932287, 342608596111, 1702289233577, 7464047307389, 37117102285215, 163889023336193, 815531984477949, 3622301825830109, 18034891620843507, 80511836008740271

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A259205 A149641 A149642 * A149644 A149645 A149646

Adjacent sequences: A149640 A149641 A149642 * A149644 A149645 A149646

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved