A149332 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, 0, 0), (0, -1, 0), (0, 1, -1), (0, 1, 1), (1, 0, -1)}.

1, 1, 4, 12, 40, 142, 540, 2041, 7964, 31688, 128670, 524420, 2169274, 9053525, 38159532, 161479853, 688930108, 2954700204, 12747388511, 55173583722, 240023881585, 1047906743361, 4593155392198, 20183907755541, 89004497784108, 393504692416187, 1744708316146483, 7751349113436365

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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, 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: A259806 A100320 A064649 * A149333 A074032 A074450

Adjacent sequences: A149329 A149330 A149331 * A149333 A149334 A149335

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved