A150861 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, 1), (0, 1, -1), (0, 1, 1), (1, -1, 1), (1, 0, 1)}

1, 2, 8, 32, 143, 642, 2998, 14072, 67242, 322573, 1562132, 7587183, 37053764, 181362866, 890748249, 4382280763, 21608774431, 106691560796, 527608687921, 2611785344601, 12943557247057, 64197546373532, 318674512985846, 1582897145724556, 7867473584751838, 39123624559355396, 194651807194055726

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A150860 A308368 A072243 * A150862 A150863 A084137

Adjacent sequences: A150858 A150859 A150860 * A150862 A150863 A150864

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved