A150872 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, 0), (0, 0, 1), (1, -1, 1), (1, 0, -1), (1, 1, 1)}.

1, 2, 8, 33, 146, 658, 3029, 14115, 66456, 315187, 1503673, 7206799, 34672709, 167340770, 809789185, 3927612703, 19087000864, 92915803145, 452996664725, 2211463585742, 10808909971929, 52886985482703, 259021496242816, 1269709778949934, 6229045905291431, 30581448347680104, 150241063646646508

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A150869 A150870 A150871 * A150873 A150874 A150875

Adjacent sequences: A150869 A150870 A150871 * A150873 A150874 A150875

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved