A149934 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, 1, 1), (0, 1, 0), (1, 0, 0)}.

1, 2, 5, 15, 49, 165, 590, 2198, 8243, 31318, 122159, 481187, 1906550, 7641233, 30899086, 125343131, 512017159, 2105778549, 8688607252, 35963536047, 149624482747, 624448244685, 2612364697842, 10963368933624, 46144530334887, 194563664904657, 822272491695293, 3483175115695255

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, k, -1 + n] + aux[1 + i, -1 + 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: A149931 A149932 A149933 * A348666 A149935 A149936

Adjacent sequences: A149931 A149932 A149933 * A149935 A149936 A149937

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved