A148035 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, 0, 1), (-1, 1, -1), (1, -1, 0), (1, 0, 0)}.

1, 1, 2, 3, 8, 17, 53, 126, 431, 1141, 4046, 11293, 42267, 125308, 476076, 1453581, 5712452, 18140643, 71884868, 232645573, 943383733, 3139026545, 12795771881, 43148544469, 178859656585, 615743018905, 2561534313985, 8906628231923, 37528126025030, 132601880616631, 560156057424649, 1994657576103465

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A148032 A148033 A148034 * A148036 A148037 A345324

Adjacent sequences: A148032 A148033 A148034 * A148036 A148037 A148038

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved