A149273 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, 0, -1), (1, 1, 1)}.

1, 1, 4, 11, 42, 132, 520, 1761, 6970, 24604, 97740, 353886, 1408456, 5186830, 20673334, 77060191, 307402490, 1156225566, 4615394884, 17481280422, 69812708258, 265891539128, 1062228300604, 4063922007022, 16239378774724, 62361864245180, 249247207795482, 960167359575770, 3838172631009646

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 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: A151273 A149271 A149272 * A149274 A151427 A149275

Adjacent sequences: A149270 A149271 A149272 * A149274 A149275 A149276

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved