A149848 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, -1, 0), (-1, 0, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 4, 14, 46, 144, 540, 1924, 6954, 27006, 100678, 388228, 1533052, 5922870, 23618486, 94259276, 374458076, 1520059574, 6128989460, 24855713538, 101883235332, 415282905284, 1708382176020, 7047461328028, 29031380650850, 120544525962236, 500065373325584, 2079111915005852, 8685156055182124

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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, 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] + 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: A070822 A101536 A149847 * A149849 A149850 A255502

Adjacent sequences: A149845 A149846 A149847 * A149849 A149850 A149851

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved