A148389 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, 0), (-1, 1, 1), (0, 1, -1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 5, 16, 51, 175, 603, 2179, 7966, 30115, 115175, 447599, 1754566, 6960211, 27838776, 112401002, 457156790, 1872092533, 7709515518, 31925277406, 132858964434, 555535209096, 2332992606313, 9836786434533, 41626228814418, 176751460040269, 752917025247036, 3216949479854651

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[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A054660 A231296 A148388 * A108529 A268213 A231357

Adjacent sequences: A148386 A148387 A148388 * A148390 A148391 A148392

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved