A148500 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), (0, 0, 1), (0, 1, -1), (1, 0, -1)}.

1, 1, 3, 5, 15, 33, 109, 279, 949, 2605, 9109, 26629, 94979, 288391, 1041801, 3269639, 11955911, 38443705, 141695339, 465029111, 1727437497, 5764533389, 21534026857, 72876464863, 273704178283, 937530491617, 3535944360787, 12237394498215, 46335364759251, 161828293844907, 614742052374589, 2164093416172221

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A186341 A262326 A148499 * A148501 A148502 A295614

Adjacent sequences: A148497 A148498 A148499 * A148501 A148502 A148503

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved