A151166 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), (1, 0, 0), (1, 0, 1), (1, 1, 0)}

1, 3, 12, 47, 210, 917, 4241, 19289, 91082, 424450, 2027095, 9587202, 46150620, 220465569, 1067112006, 5134405566, 24954205199, 120707011116, 588521772260, 2858465210452, 13971871660818, 68081463353918, 333456746083175, 1629097418331777, 7992707142999983, 39131997344447207, 192264632552488727

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 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: A151163 A151164 A151165 * A151167 A064562 A259865

Adjacent sequences: A151163 A151164 A151165 * A151167 A151168 A151169

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved