A148672 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, 3, 7, 21, 62, 201, 633, 2039, 6740, 22605, 76638, 260854, 899130, 3106961, 10801535, 37807635, 132935072, 469231691, 1660888854, 5907569428, 21056698312, 75251862261, 269722099238, 969177576954, 3490118514190, 12590156324230, 45524702976470, 164856574519094, 597947942363506, 2172466763369937

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, -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: A369528 A148670 A148671 * A148673 A141495 A151412

Adjacent sequences: A148669 A148670 A148671 * A148673 A148674 A148675

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved