A148961 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, 1, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 9, 31, 103, 407, 1533, 6125, 24959, 103117, 433129, 1849783, 7940861, 34601631, 151634999, 669851379, 2981419261, 13336184581, 60013632895, 271390475929, 1232328156283, 5621144521081, 25728998626719, 118185644696375, 544659217150797, 2517177874501327, 11666766786541973, 54209981549820651

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + 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: A148960 A027029 A027092 * A148962 A148963 A027031

Adjacent sequences: A148958 A148959 A148960 * A148962 A148963 A148964

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved