A150787 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, 0), (1, 0, -1), (1, 0, 0), (1, 1, 1)}

1, 2, 8, 30, 136, 578, 2729, 12297, 59170, 274909, 1337955, 6335345, 31052823, 148900795, 733293712, 3547179137, 17527323964, 85330022249, 422654866104, 2067558396785, 10259587177893, 50374101955177, 250312179804229, 1232593520556286, 6131458742986123, 30262702145332219, 150668646422483374

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, -1 + j, 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: A150785 A036723 A150786 * A150788 A150789 A150790

Adjacent sequences: A150784 A150785 A150786 * A150788 A150789 A150790

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved