A149667 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, 0), (0, -1, 1), (0, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 63, 251, 1021, 4229, 17763, 75495, 324419, 1405651, 6129959, 26885263, 118546757, 525145593, 2335550797, 10423483181, 46668994497, 209568731239, 943579928523, 4258648662289, 19262899227221, 87309837723849, 396489947776471, 1803702183461177, 8218756170526909, 37506891842655889

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[i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A051736 A301560 A099528 * A149668 A149669 A149670

Adjacent sequences: A149664 A149665 A149666 * A149668 A149669 A149670

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved