A149328 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, 0), (0, 1, -1), (1, 0, -1), (1, 0, 1)}.

1, 1, 4, 12, 39, 142, 545, 2106, 8382, 34215, 142643, 600014, 2557631, 11028505, 48020121, 210769413, 931363949, 4143384678, 18544445680, 83436432216, 377186393627, 1712438625809, 7806272131532, 35718243832372, 163985930358341, 755228559001683, 3488271916047151, 16155889488916942

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A334458 A122920 A241073 * A149329 A149330 A149331

Adjacent sequences: A149325 A149326 A149327 * A149329 A149330 A149331

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved