A149892 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, 0, 1), (0, 1, 0), (1, 1, -1)}.

1, 2, 5, 14, 45, 154, 551, 2028, 7665, 29584, 116265, 463700, 1873033, 7648340, 31530533, 131079720, 549015129, 2314905316, 9819648969, 41881655112, 179516554153, 772952073692, 3342001719279, 14505229617986, 63180178810125, 276098296632942, 1210245835681237, 5320115750281586

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, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A149889 A149890 A149891 * A149893 A149894 A030126

Adjacent sequences: A149889 A149890 A149891 * A149893 A149894 A149895

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved