A150786 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, 0), (1, 0, 0), (1, 1, -1), (1, 1, 1)}.

1, 2, 8, 30, 136, 570, 2666, 11810, 56202, 256598, 1232487, 5735225, 27726387, 130699845, 634668095, 3019779028, 14713965181, 70500519263, 344415946439, 1659196210333, 8122930459813, 39300262731933, 192736850009887, 935757803976718, 4595887028717244, 22377876932689454, 110043717399426404

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + 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: A150784 A150785 A036723 * A150787 A150788 A150789

Adjacent sequences: A150783 A150784 A150785 * A150787 A150788 A150789

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved