A149860 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), (0, 1, -1), (1, 0, 0)}.

1, 2, 5, 13, 38, 127, 439, 1561, 5673, 21144, 81137, 314145, 1232603, 4909110, 19728702, 80154126, 327820102, 1350493841, 5610705828, 23416574546, 98304768279, 414909948960, 1758260345077, 7488145688244, 32001010966712, 137249426117898, 590954969322700, 2551267808790323, 11049608193888765

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, k, -1 + n] + aux[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, 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: A148304 A149859 A000800 * A006823 A319378 A151446

Adjacent sequences: A149857 A149858 A149859 * A149861 A149862 A149863

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved