A149471 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), (-1, 0, 1), (1, -1, 1), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 13, 55, 206, 929, 3854, 17797, 77497, 364043, 1636237, 7772563, 35679961, 170863707, 796256786, 3836089543, 18077155221, 87495240136, 415839255346, 2020128721725, 9665396470341, 47094220547527, 226531339610481, 1106476770045798, 5345538685045776, 26163552380725908, 126854484533770709

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149469 A229182 A149470 * A149472 A149473 A365854

Adjacent sequences: A149468 A149469 A149470 * A149472 A149473 A149474

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved