A150849 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, 0, 0), (0, -1, 0), (0, 1, 0), (1, 1, -1), (1, 1, 1)}.

1, 2, 8, 32, 140, 624, 2835, 13067, 60938, 286498, 1356904, 6459691, 30892611, 148291664, 714120564, 3448426056, 16692404388, 80968662585, 393478911192, 1915279956230, 9336406678901, 45571836417430, 222704732448507, 1089503921232924, 5335248476500528, 26149843216648124, 128274792913583856

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A150846 A150847 A150848 * A150850 A179469 A150851

Adjacent sequences: A150846 A150847 A150848 * A150850 A150851 A150852

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved