A150820 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), (1, 0, -1), (1, 0, 0), (1, 1, 1)}

1, 2, 8, 31, 141, 610, 2860, 12992, 61918, 288651, 1388824, 6576019, 31836080, 152292256, 740484620, 3567625444, 17402537091, 84284773469, 412155668864, 2004121183677, 9819698813265, 47897239355040, 235066965446717, 1149436188118396, 5648823473420351, 27677996959957284, 136179636076655510

Offset

0,2

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, j, k, -1 + n] + aux[-1 + i, 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: A150819 A003175 A129427 * A150821 A150822 A150823

Adjacent sequences: A150817 A150818 A150819 * A150821 A150822 A150823

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved