A150877 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, 0, 1), (0, -1, 1), (0, 1, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 8, 33, 147, 676, 3166, 15053, 72206, 349108, 1696935, 8285899, 40599296, 199495622, 982557165, 4848579417, 23964666699, 118608352543, 587706742771, 2914968510910, 14470269525829, 71885142979166, 357339121440144, 1777321735893479, 8844357043484105, 44030751078285280, 219287581858809457

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150874 A150875 A150876 * A150878 A150879 A150880

Adjacent sequences: A150874 A150875 A150876 * A150878 A150879 A150880

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved