A148579 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, 0, 1), (1, 0, -1)}.

1, 1, 3, 6, 20, 51, 184, 552, 2112, 7007, 27770, 97954, 397618, 1465253, 6064186, 23118215, 97170678, 380318302, 1618291003, 6467714046, 27801600440, 113039060164, 490098103728, 2021518407162, 8829111125199, 36862439853648, 162021554794771, 683535234262247, 3021023205814566

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, j, 1 + k, -1 + n] + aux[i, j, -1 + 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: A148577 A148578 A182299 * A151263 A148580 A148581

Adjacent sequences: A148576 A148577 A148578 * A148580 A148581 A148582

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved