A150584 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, 1), (0, 0, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 26, 110, 469, 2110, 9539, 44207, 205708, 969920, 4588869, 21880774, 104624543, 502768044, 2421529307, 11702566048, 56660506153, 274998864288, 1336740579684, 6509513954956, 31739731297084, 154976524378720, 757517079987287, 3706840240394039, 18155479106144526, 89003665124938127

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150581 A150582 A150583 * A150585 A150586 A196709

Adjacent sequences: A150581 A150582 A150583 * A150585 A150586 A150587

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved