A149869 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, 1, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 5, 13, 42, 138, 482, 1654, 6153, 22665, 86602, 325298, 1282358, 4990247, 19921217, 78358303, 318886120, 1281888719, 5254017106, 21261292818, 88301518722, 362702052232, 1513168885596, 6243268426298, 26300445746536, 109710928573843, 463595936683840, 1940069540427649, 8259430332344895

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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + 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: A096724 A088553 A262934 * A149870 A149871 A149872

Adjacent sequences: A149866 A149867 A149868 * A149870 A149871 A149872

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved