A149936 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, 1, -1), (0, 1, 0), (1, 0, 0)}.

1, 2, 5, 15, 49, 166, 595, 2213, 8406, 32659, 129460, 520077, 2115561, 8708598, 36177828, 151509307, 639429106, 2716329348, 11605358103, 49852770845, 215189799958, 932874529705, 4060478312656, 17739483864132, 77761392840316, 341940145521114, 1508018811658406, 6668596177504285

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, -1 + 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: A149934 A348666 A149935 * A189176 A366054 A369631

Adjacent sequences: A149933 A149934 A149935 * A149937 A149938 A149939

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved