A151037 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, 1, -1), (0, 0, 1), (0, 1, 0), (1, 0, 0)}.

1, 3, 9, 31, 117, 461, 1875, 7807, 33115, 142517, 620337, 2725701, 12071605, 53820411, 241320911, 1087364591, 4920600571, 22351035079, 101865024915, 465632154641, 2134115850465, 9804736650791, 45143823225037, 208266791273933, 962557785199341, 4456086691240197, 20660610624854463, 95927834225565477

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, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A151035 A151036 A073724 * A371724 A066571 A087648

Adjacent sequences: A151034 A151035 A151036 * A151038 A151039 A151040

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved