A150882 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, 1), (0, 0, 1), (1, -1, 1), (1, 0, -1), (1, 1, 1)}.

1, 2, 8, 33, 149, 671, 3124, 14572, 69027, 327738, 1568883, 7526367, 36282157, 175229271, 848963109, 4119569655, 20033898783, 97555323988, 475811775727, 2323275614661, 11358048112728, 55579446613429, 272240840947922, 1334566048873148, 6547544693115974, 32145195316547195, 157924212566811068

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150880 A150881 A053817 * A150883 A150884 A150885

Adjacent sequences: A150879 A150880 A150881 * A150883 A150884 A150885

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved