A148006 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, 1, -1), (1, 0, 0)}.

1, 1, 2, 3, 8, 15, 44, 91, 300, 675, 2246, 5225, 18369, 44590, 157351, 389281, 1418064, 3598815, 13127212, 33721485, 125539307, 327997148, 1221478559, 3218359939, 12154464884, 32412375855, 122407772319, 328464178536, 1253012930330, 3392521591292, 12940473812157, 35205364700389, 135293932230274

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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[1 + 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: A156802 A148005 A151394 * A148007 A148008 A148009

Adjacent sequences: A148003 A148004 A148005 * A148007 A148008 A148009

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved