A148714 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, 1), (1, 0, -1), (1, 1, 0)}.

1, 1, 3, 7, 24, 67, 247, 762, 2895, 9497, 36627, 124992, 486807, 1707285, 6693429, 23951625, 94333590, 342762753, 1354438586, 4980627013, 19729351523, 73247980483, 290692026962, 1087691576455, 4322826784048, 16279785225723, 64774066504350, 245267148495207, 976746419471146, 3715545792176250

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, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A145542 A071108 A148713 * A148715 A148716 A148717

Adjacent sequences: A148711 A148712 A148713 * A148715 A148716 A148717

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved