A148951 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), (0, 1, -1), (1, 0, -1), (1, 1, 0)}.

1, 1, 3, 9, 30, 102, 397, 1500, 6009, 24451, 101183, 425673, 1816275, 7816634, 34052901, 149363641, 660504469, 2940315586, 13164619889, 59271046961, 268144561326, 1218435897550, 5559533877874, 25460075683483, 117000817561805, 539378629640900, 2493853152959533, 11562252045813059, 53742395325404286

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A148948 A148949 A148950 * A228248 A047064 A047007

Adjacent sequences: A148948 A148949 A148950 * A148952 A148953 A148954

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved