A149630 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), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 15, 67, 265, 1181, 5035, 22891, 101385, 467833, 2124239, 9908627, 45726667, 215107819, 1004102949, 4755098001, 22389176879, 106594259895, 505286078225, 2416188580561, 11515108092133, 55264506834405, 264539724909511, 1273537032925423, 6118479896286207, 29533597410434055, 142327445758987571

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + 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: A149627 A149628 A149629 * A149631 A079569 A149632

Adjacent sequences: A149627 A149628 A149629 * A149631 A149632 A149633

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved