A148007 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, -1, 0), (-1, 0, 1), (-1, 1, -1), (1, 0, 0)}.

1, 1, 2, 3, 8, 15, 44, 91, 314, 717, 2462, 5786, 20723, 50596, 188018, 473183, 1804072, 4645335, 17787660, 46419584, 181375177, 481275126, 1911271468, 5141399599, 20539168658, 55762292565, 224393416829, 614548182426, 2502149168249, 6916703340431, 28335787685261, 78869864682145, 324320769451124

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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, j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A148005 A151394 A148006 * A148008 A148009 A148010

Adjacent sequences: A148004 A148005 A148006 * A148008 A148009 A148010

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved