A149019 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, 1), (1, 1, -1), (1, 1, 0)}.

1, 1, 3, 9, 35, 131, 539, 2178, 9466, 39944, 178102, 779382, 3535378, 15837243, 72810285, 331162556, 1538465914, 7082275082, 33160005984, 154175852070, 726421380590, 3403523284138, 16121460813022, 75997260757594, 361573678921754, 1713363345487223, 8182019330408203, 38944062120025760

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, 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, -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: A149016 A149017 A149018 * A102865 A046697 A151045

Adjacent sequences: A149016 A149017 A149018 * A149020 A149021 A149022

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved