A150763 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), (0, -1, 0), (0, 1, -1), (0, 1, 1), (1, 1, 0)}

1, 2, 8, 30, 124, 526, 2293, 10151, 45611, 207164, 948963, 4379129, 20334454, 94910832, 445014609, 2094881198, 9896041051, 46892548781, 222820230769, 1061429069122, 5067647230070, 24244574605490, 116208774713007, 557969923616332, 2683310444822610, 12923126174542911, 62323796793505182

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, 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: A150762 A074026 A054663 * A054662 A150764 A150765

Adjacent sequences: A150760 A150761 A150762 * A150764 A150765 A150766

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved