A150818 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), (0, 1, -1), (1, 0, 0), (1, 1, 1)}

1, 2, 8, 31, 136, 603, 2762, 12762, 59796, 282112, 1340577, 6401082, 30701136, 147752628, 713229089, 3451491228, 16739404303, 81337802668, 395887118980, 1929701874676, 9418489826558, 46024023964585, 225139138344005, 1102394618779217, 5402637900253288, 26498720939616348, 130066658818109547

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, 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, -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: A150815 A150816 A150817 * A009567 A150819 A003175

Adjacent sequences: A150815 A150816 A150817 * A150819 A150820 A150821

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved