A149534 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, 0, -1), (0, -1, 0), (1, -1, 0), (1, 1, 1)}

1, 1, 5, 13, 49, 177, 667, 2511, 10009, 39187, 155965, 634409, 2572311, 10467813, 43375789, 178967139, 740636461, 3103154817, 12965474087, 54264996479, 229254996155, 966417702403, 4079049705641, 17340341569785, 73594562906139, 312632789194025, 1335568546118335, 5698403070572647

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, k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A084601 A149532 A149533 * A149535 A149536 A149537

Adjacent sequences: A149531 A149532 A149533 * A149535 A149536 A149537

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved