A150718 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), (1, 0, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 8, 28, 116, 465, 2002, 8437, 37237, 161422, 722872, 3193287, 14438915, 64628012, 294304218, 1330034420, 6090094043, 27725305017, 127515229293, 583875027223, 2695253214088, 12398866699006, 57412413236322, 265130888541365, 1230934711860059, 5702885873267887, 26537994068161571, 123289342436536590

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, 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, 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: A150716 A151299 A150717 * A344558 A217720 A151300

Adjacent sequences: A150715 A150716 A150717 * A150719 A150720 A150721

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved