A149558 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, 1, -1), (1, -1, 0), (1, 1, 1)}

1, 1, 5, 13, 59, 193, 895, 3259, 15359, 58873, 280173, 1113879, 5348147, 21804729, 105287385, 437178569, 2120520381, 8935434007, 43498711149, 185440154245, 905220919951, 3896089055715, 19062269002521, 82711407198491, 405451224884227, 1771346414264423, 8696751070014109, 38219970873869521

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, 1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A149555 A149556 A149557 * A149559 A149560 A149561

Adjacent sequences: A149555 A149556 A149557 * A149559 A149560 A149561

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved