A150765 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), (0, 0, -1), (1, 0, 0), (1, 1, 1)}

1, 2, 8, 30, 126, 539, 2358, 10526, 47621, 217182, 1002081, 4644109, 21682588, 101701604, 478985355, 2265535437, 10747214934, 51142755153, 244020287947, 1166918590405, 5593066651598, 26857013016864, 129196968427815, 622526449929799, 3003950035203570, 14515880870236575, 70231930830344139

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[i, 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: A150763 A054662 A150764 * A150766 A150767 A150768

Adjacent sequences: A150762 A150763 A150764 * A150766 A150767 A150768

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved