A151241 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, 0, 0), (-1, 0, 1), (1, 0, 0), (1, 0, 1), (1, 1, 0)}.

1, 3, 15, 63, 315, 1431, 7155, 33615, 168075, 804087, 4020435, 19448991, 97244955, 473907591, 2369537955, 11607504687, 58037523435, 285383915415, 1426919577075, 7036602369471, 35183011847355, 173883879452583, 869419397262915, 4304442210846543, 21522211054232715, 106705461576611511

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A111303 A118339 A083858 * A080948 A098102 A144067

Adjacent sequences: A151238 A151239 A151240 * A151242 A151243 A151244

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved