A149622 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, -1), (1, 1, 1)}.

1, 1, 5, 15, 65, 249, 1071, 4559, 20009, 88587, 397369, 1796375, 8202769, 37639895, 173955497, 807209165, 3764198105, 17620920645, 82776073951, 390099799289, 1843525688345, 8734856806545, 41485574839385, 197454847189457, 941691651702921, 4499177052380199, 21532549627421749, 103214775664543729

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, 1 + 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: A149619 A149620 A149621 * A247281 A149623 A149624

Adjacent sequences: A149619 A149620 A149621 * A149623 A149624 A149625

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved