A148449 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, 0), (-1, 1, 1), (0, 1, 1), (1, 0, -1)}.

1, 1, 2, 6, 17, 50, 171, 569, 1990, 7154, 25959, 96603, 363241, 1381671, 5322075, 20650133, 80879351, 318931686, 1265735372, 5054541248, 20286564666, 81831126986, 331530026432, 1348625601656, 5506975413853, 22564173676309, 92754771845149, 382423288873579, 1581116395807010, 6554162896744539

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A356783 A148447 A148448 * A148450 A153773 A059398

Adjacent sequences: A148446 A148447 A148448 * A148450 A148451 A148452

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved