A150873 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, 0, 1), (0, 1, -1), (1, 1, 1)}.

1, 2, 8, 33, 147, 657, 3040, 14101, 66486, 314372, 1499644, 7171861, 34481451, 166138901, 803280189, 3890825365, 18891672745, 91864473277, 447507922130, 2182706530025, 10660708576682, 52123282635004, 255123911489477, 1249844069668792, 6128402058798688, 30072370302068910, 147676260877363755

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[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A150870 A150871 A150872 * A150874 A150875 A150876

Adjacent sequences: A150870 A150871 A150872 * A150874 A150875 A150876

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved