A149537 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, 0), (-1, 1, -1), (0, 1, -1), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 13, 49, 177, 667, 2543, 10041, 39539, 158603, 639927, 2607159, 10666927, 43932533, 181850695, 755611295, 3151697829, 13194669577, 55399106349, 233230763877, 984474496333, 4165302588113, 17658641745695, 75013802642433, 319243175216361, 1360852049360291, 5810001118731197

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[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A149534 A149535 A149536 * A146689 A146657 A243304

Adjacent sequences: A149534 A149535 A149536 * A149538 A149539 A149540

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved