A150847 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, 1), (0, 1, 1), (1, 0, -1), (1, 1, 1)}.

1, 2, 8, 32, 140, 617, 2825, 12989, 60799, 285605, 1355212, 6448778, 30876524, 148182226, 714046275, 3447484841, 16691884243, 80949584877, 393388278159, 1914344878230, 9330462585841, 45528694065925, 222436937930322, 1087807926738612, 5325191050098931, 26090385582013999, 127934831995426037

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, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A151828 A150845 A150846 * A150848 A150849 A150850

Adjacent sequences: A150844 A150845 A150846 * A150848 A150849 A150850

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved