A149962 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, 0), (1, 0, 0)}.

1, 2, 5, 16, 54, 191, 708, 2691, 10500, 41709, 167949, 686327, 2833422, 11805214, 49617037, 209963526, 894400402, 3831980642, 16499883222, 71390792327, 310181111919, 1352902241363, 5922364156483, 26008930393279, 114573064355346, 506138029794659, 2241723481851415, 9953362142887318

Offset

0,2

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, k, -1 + n] + aux[i, -1 + j, 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: A149960 A149961 A141754 * A149963 A149964 A148399

Adjacent sequences: A149959 A149960 A149961 * A149963 A149964 A149965

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved