A150951 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, 1, 1), (0, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 35, 155, 688, 3163, 14608, 68442, 323007, 1534140, 7318363, 35087119, 168746710, 813977051, 3936697604, 19082459598, 92671351366, 450828322591, 2196603187071, 10717007182966, 52350759519615, 256013137943151, 1253242895804371, 6140494021718587, 30111953154533101, 147778132547086164

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, -1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A150948 A150949 A150950 * A150952 A150953 A150954

Adjacent sequences: A150948 A150949 A150950 * A150952 A150953 A150954

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved