A148336 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, 0, 1), (0, 1, -1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 5, 14, 44, 152, 538, 1995, 7662, 29940, 120398, 491459, 2038747, 8581283, 36510595, 157045874, 681735158, 2982964821, 13151583858, 58359139202, 260520699938, 1169379642893, 5274592297251, 23900749201570, 108751720395298, 496735253829031, 2276991119469184, 10471775432100043

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, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A149885 A149886 A207081 * A257273 A119021 A002890

Adjacent sequences: A148333 A148334 A148335 * A148337 A148338 A148339

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved