A150910 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, 0), (-1, 1, -1), (1, -1, 0), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 31, 145, 587, 2791, 12106, 58124, 261744, 1264717, 5828785, 28292206, 132437321, 645033524, 3053061983, 14909656701, 71152742334, 348223759551, 1672326960269, 8198958472117, 39571030467943, 194295312406676, 941486927645661, 4628620226911394, 22502035601784115, 110748086623000399

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, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A150907 A150908 A150909 * A150911 A150912 A165653

Adjacent sequences: A150907 A150908 A150909 * A150911 A150912 A150913

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved