A149601 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, 0, 0), (1, -1, -1), (1, 1, -1), (1, 1, 1)}

1, 1, 5, 15, 61, 221, 961, 3843, 16691, 69321, 309193, 1326193, 5933567, 25855481, 117273025, 519449575, 2361947235, 10553854571, 48388079905, 218345888851, 1003023976695, 4551161057929, 21023406034253, 96016404138687, 444214179768713, 2036543544957007, 9459583710294399, 43569389164709415

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A149600 A369555 A207969 * A149602 A149603 A149604

Adjacent sequences: A149598 A149599 A149600 * A149602 A149603 A149604

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved