A149587 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, 1, -1), (0, 0, -1), (1, -1, 0), (1, 1, 1)}

1, 1, 5, 15, 55, 215, 881, 3499, 14705, 62815, 267691, 1152031, 5054975, 22215495, 97820089, 435083549, 1946783755, 8714538577, 39182038837, 177168174583, 802527055581, 3641247264783, 16585238682009, 75740989879295, 346271384506611, 1586505453816213, 7287225822759371, 33516216036717503

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[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A114947 A316104 A149586 * A149588 A137959 A001552

Adjacent sequences: A149584 A149585 A149586 * A149588 A149589 A149590

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved