A149317 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, 0, 1), (-1, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 11, 52, 170, 820, 2959, 14514, 55611, 274519, 1091963, 5413275, 22125974, 109968669, 458527130, 2282677742, 9666067566, 48176053055, 206527439304, 1030152690801, 4460625399845, 22262288594871, 97203545438273, 485331216939480, 2134048347102848, 10658501929003342, 47149574060250334

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + 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: A318120 A355337 A218957 * A027042 A051770 A262006

Adjacent sequences: A149314 A149315 A149316 * A149318 A149319 A149320

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved