A149796 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, 0, 1), (-1, 1, 1), (0, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 19, 85, 375, 1731, 7933, 37317, 175613, 834751, 3978767, 19088985, 91734763, 442665273, 2140092773, 10374076975, 50362478267, 244991588713, 1193270320801, 5820678164441, 28423633358011, 138963703630997, 680011807254599, 3330802581469895, 16327645188536235, 80101834588157793

Offset

0,3

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, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A282707 A149794 A149795 * A348410 A005191 A324595

Adjacent sequences: A149793 A149794 A149795 * A149797 A149798 A149799

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved