A151039 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), (0, 1, 0), (0, 1, 1), (1, 0, 0)}.

1, 3, 9, 33, 129, 501, 2062, 8683, 36371, 156786, 683812, 2970272, 13128686, 58445192, 259361838, 1164616878, 5254843629, 23651403474, 107365109937, 489088828144, 2223545646021, 10174666599524, 46681466839310, 213826957872209, 984446447446364, 4541754228573514, 20925283362844245, 96805879272199949

Offset

0,2

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 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: A049176 A049151 A254036 * A151040 A151041 A151042

Adjacent sequences: A151036 A151037 A151038 * A151040 A151041 A151042

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved