A149331 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, 1), (-1, 1, 0), (0, 0, -1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 12, 39, 154, 607, 2337, 9605, 40746, 169774, 721592, 3141676, 13672351, 59571861, 263497047, 1172340186, 5211997832, 23318908785, 105062899783, 473849638986, 2141396641379, 9726873352911, 44297573024958, 201921039952754, 923000948331317, 4231449484191799, 19421192737753899

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A149328 A149329 A149330 * A009532 A248325 A344122

Adjacent sequences: A149328 A149329 A149330 * A149332 A149333 A149334

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved