A148589 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), (0, 1, -1), (1, 0, -1)}.

1, 1, 3, 6, 20, 55, 196, 639, 2327, 8256, 30927, 115956, 447505, 1732101, 6831117, 27059859, 108748569, 439260818, 1790252423, 7336642698, 30255128337, 125497752360, 523152712624, 2190695840636, 9213349157790, 38891208523916, 164839756761025, 700926280501146, 2990200877058031

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A148587 A186409 A148588 * A148590 A363592 A148591

Adjacent sequences: A148586 A148587 A148588 * A148590 A148591 A148592

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved