A148663 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, 1, 1), (1, 0, 0), (1, 1, -1)}

1, 1, 3, 6, 25, 69, 306, 968, 4495, 15457, 73187, 265886, 1276200, 4822808, 23356328, 90916036, 443070045, 1764876843, 8640616651, 35059209106, 172241437579, 709515169465, 3495119780527, 14580289703320, 71975955298661, 303483724749584, 1500714793344535, 6386054657765297, 31622910371957637

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[1 + i, -1 + 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: A148660 A148661 A148662 * A361288 A266549 A057730

Adjacent sequences: A148660 A148661 A148662 * A148664 A148665 A148666

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved