A151219 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, 1, 1), (1, 0, 1), (1, 1, 0), (1, 1, 1)}

1, 3, 13, 55, 265, 1205, 5941, 27961, 138745, 665103, 3310317, 16041609, 79986407, 390348973, 1948432333, 9555608427, 47726348731, 234904326795, 1173682547443, 5792382066861, 28947965469611, 143162807683029, 715579210092605, 3544738294992175, 17719691563476451, 87893464730984225

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A151216 A151217 A151218 * A006225 A100588 A081952

Adjacent sequences: A151216 A151217 A151218 * A151220 A151221 A151222

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved