A149006 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, -1, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 9, 34, 120, 483, 1882, 7858, 32229, 138321, 585584, 2560197, 11082844, 49100853, 215982063, 966695396, 4303305428, 19415733580, 87237177735, 396131418000, 1793098913907, 8185259827903, 37274332989985, 170905371225916, 782158684200893, 3599711338887352, 16543367154806041

Offset

0,3

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 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: A149003 A149004 A149005 * A149007 A053791 A296223

Adjacent sequences: A149003 A149004 A149005 * A149007 A149008 A149009

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved