A149968 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), (0, 1, -1), (0, 1, 0), (1, 0, 1)}.

1, 2, 5, 16, 55, 188, 674, 2471, 9067, 33926, 128156, 484224, 1847218, 7084777, 27186054, 104885416, 405958461, 1572023508, 6108058902, 23783305717, 92648913045, 361724652715, 1414358846767, 5532545855330, 21675406458263, 85011660185348, 333545750611017, 1310157468147696, 5150459680441075

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[i, -1 + j, k, -1 + n] + aux[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: A108526 A363201 A321470 * A149969 A051960 A149970

Adjacent sequences: A149965 A149966 A149967 * A149969 A149970 A149971

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved