A150615 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, 0, 0), (0, 1, 0), (1, 1, -1), (1, 1, 1)}.

1, 2, 7, 27, 113, 474, 2051, 9054, 40713, 184664, 844547, 3891253, 18059049, 84270068, 394979919, 1858490051, 8777146689, 41589213864, 197626125243, 941429903019, 4494972448993, 21507534756544, 103108934983103, 495176509211198, 2381865856324601, 11474143461250934, 55350964318327831, 267354109620623169

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, 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: A150614 A182454 A192455 * A150616 A150617 A150618

Adjacent sequences: A150612 A150613 A150614 * A150616 A150617 A150618

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved