A149878 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, 0, 1), (0, 1, 0), (1, -1, 0)}.

1, 2, 5, 14, 42, 140, 480, 1710, 6227, 23087, 87495, 335253, 1304117, 5120189, 20286069, 81087950, 326175588, 1321918434, 5385669252, 22062590893, 90821095614, 375419697147, 1558667802107, 6493810637583, 27152832780694, 113894033778109, 479137002109941, 2021504946377131, 8550206541089202

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, 1 + j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A306422 A052853 A149877 * A148332 A000751 A000744

Adjacent sequences: A149875 A149876 A149877 * A149879 A149880 A149881

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved