A148245 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), (1, -1, 1), (1, 0, 0)}.

1, 1, 2, 4, 13, 36, 118, 385, 1347, 4793, 17541, 65636, 250216, 967021, 3797305, 15065117, 60472135, 244972973, 1000682072, 4120934958, 17084483793, 71285735974, 299214894796, 1262451255497, 5353653191585, 22805887265592, 97559616492228, 419020906728549, 1806219820808517, 7812824361279408

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[-1 + 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: A148242 A148243 A148244 * A148246 A148247 A148248

Adjacent sequences: A148242 A148243 A148244 * A148246 A148247 A148248

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved