A149808 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, 0, 0), (-1, 1, 1), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 19, 91, 391, 1911, 8745, 43141, 203145, 1007609, 4826733, 24013317, 116273537, 579500509, 2826359467, 14101820227, 69129752095, 345154523255, 1698332231795, 8483340867615, 41859508101555, 209155092781463, 1034270680208087, 5168880642818399, 25603548543186475, 127974318768638411

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149805 A149806 A149807 * A371836 A149809 A263245

Adjacent sequences: A149805 A149806 A149807 * A149809 A149810 A149811

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved