A149269 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, 0), (0, 0, -1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 11, 41, 148, 576, 2276, 9235, 38109, 159744, 676538, 2900033, 12524567, 54531416, 238998571, 1053340722, 4667557784, 20776709880, 92863035709, 416671461742, 1875769725307, 8470981644785, 38364925789237, 174201019952436, 792929797217149, 3617286871935752, 16535853712546563

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A281346 A030981 A151455 * A149270 A306188 A307702

Adjacent sequences: A149266 A149267 A149268 * A149270 A149271 A149272

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved