A149169 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, -1), (-1, 1, 1), (1, -1, 0), (1, 1, 0)}.

1, 1, 4, 9, 42, 130, 610, 2095, 10150, 37696, 182974, 707948, 3478480, 13945828, 68567200, 280881929, 1389304994, 5806737116, 28728911784, 121676284776, 604030685918, 2591257765764, 12865089610340, 55687296132644, 277050189053338, 1209869597923106, 6019537343834174, 26457591393814204

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, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A149166 A149167 A149168 * A138544 A219287 A359922

Adjacent sequences: A149166 A149167 A149168 * A149170 A149171 A149172

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved