A149704 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, 1), (0, 1, -1), (1, -1, 0), (1, 1, 1)}.

1, 1, 5, 17, 69, 283, 1221, 5331, 23769, 107001, 487945, 2243869, 10383885, 48373479, 226576711, 1065750707, 5033216081, 23855847143, 113417165091, 540703865905, 2584161705411, 12378567019955, 59416802743749, 285720955143715, 1376328518631083, 6640284560512583, 32082470803999035, 155212758424395955

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A149702 A273331 A149703 * A273426 A149705 A149706

Adjacent sequences: A149701 A149702 A149703 * A149705 A149706 A149707

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved