A149557 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), (-1, 0, 0), (-1, 1, -1), (1, -1, 0), (1, 1, 1)}

1, 1, 5, 13, 59, 193, 895, 3259, 15291, 58641, 278023, 1107235, 5295601, 21602507, 103888769, 431979255, 2088322907, 8809419485, 42735313349, 182391672799, 887657036207, 3825232735637, 18661736385173, 81064401244013, 396325426798887, 1733517914129193, 8490333231128203, 37355022085126659

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, 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: A149554 A149555 A149556 * A149558 A149559 A149560

Adjacent sequences: A149554 A149555 A149556 * A149558 A149559 A149560

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved