A149052 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, 1, 0), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 10, 40, 152, 663, 2764, 12535, 54868, 254618, 1149816, 5416066, 24963487, 118813118, 555574475, 2664192114, 12590183411, 60716475411, 289237761617, 1400959354137, 6715638325853, 32640829654516, 157247695092057, 766435077201282, 3707253492778648, 18111174831201882, 87896052331507647

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A276641 A099763 A318118 * A009692 A149053 A149054

Adjacent sequences: A149049 A149050 A149051 * A149053 A149054 A149055

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved