A148642 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), (0, 1, -1), (1, 0, 0)}.

1, 1, 3, 6, 22, 64, 227, 776, 2854, 10455, 39319, 149787, 579560, 2257337, 8887284, 35287573, 141013188, 566875691, 2292206719, 9315490488, 38020945055, 155804714945, 640940906466, 2645526853223, 10952645997032, 45477822976693, 189341279059823, 790216314543537, 3305546258574085

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, j, k, -1 + n] + aux[i, -1 + j, 1 + 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: A148639 A148640 A148641 * A049415 A208939 A209067

Adjacent sequences: A148639 A148640 A148641 * A148643 A148644 A148645

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved