A149952 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), (1, 0, 0), (1, 1, -1), (1, 1, 0)}.

1, 2, 5, 15, 50, 180, 672, 2604, 10323, 41831, 172429, 720543, 3049052, 13030183, 56185637, 244129491, 1067890597, 4699223135, 20788315074, 92400789578, 412460510507, 1848288462615, 8311490226015, 37495508818308, 169649803369283, 769655804205711, 3500411708041304, 15956530625752614

Offset

0,2

Links

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2008, 2009.

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[-1 + i, 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: A279553 A007853 A337522 * A337526 A346661 A060049

Adjacent sequences: A149949 A149950 A149951 * A149953 A149954 A149955

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved