A149012 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, 1), (0, 1, -1), (1, -1, 1), (1, 1, 0)}.

1, 1, 3, 9, 34, 128, 500, 2043, 8522, 36209, 156692, 682973, 3024637, 13504463, 60736491, 275379368, 1253735435, 5748912471, 26479707503, 122450353484, 568751348854, 2648677920527, 12384471398820, 58068692798497, 272954511504642, 1286574912244069, 6075287031732405, 28761263929036976

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A149009 A149010 A149011 * A145090 A273095 A137953

Adjacent sequences: A149009 A149010 A149011 * A149013 A149014 A149015

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved