A150204 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), (0, -1, 1), (0, 0, 1), (0, 1, 0), (1, 1, -1)}.

1, 2, 6, 21, 80, 322, 1348, 5803, 25527, 114189, 517672, 2372514, 10971518, 51120345, 239711902, 1130200367, 5353871150, 25466049605, 121567263331, 582169210310, 2795787544021, 13460137071068, 64948960877646, 314032767643989, 1521154559051834, 7380635517244799, 35865076067620553, 174522170097601855

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[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[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: A257561 A150203 A106228 * A129442 A121988 A150205

Adjacent sequences: A150201 A150202 A150203 * A150205 A150206 A150207

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved