A149986 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, 1, -1), (0, 0, 1), (1, -1, -1), (1, 1, 0)}.

1, 2, 5, 17, 55, 200, 747, 2886, 11407, 46180, 188759, 784953, 3291063, 13948318, 59537085, 256217269, 1108406473, 4826799850, 21108279413, 92791015661, 409373685603, 1813752099410, 8060179508049, 35947168744298, 160730764771703, 720860104401638, 3240196703246163, 14602369618879735

Offset

0,2

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, k, -1 + n] + aux[-1 + i, 1 + 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, 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: A149983 A149984 A149985 * A121193 A159866 A042671

Adjacent sequences: A149983 A149984 A149985 * A149987 A149988 A149989

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved