A148578 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, 0), (-1, 1, 1), (0, 0, -1), (0, 0, 1), (1, 0, -1)}.

1, 1, 3, 6, 20, 51, 182, 549, 2032, 6864, 25831, 93757, 357632, 1360284, 5277311, 20696663, 81799018, 327234487, 1316257630, 5339902882, 21808431653, 89495933691, 370048213371, 1534374902935, 6406281604192, 26815749114286, 112841852365121, 476338415205058, 2018042385135046

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, 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: A148575 A148576 A148577 * A182299 A148579 A151263

Adjacent sequences: A148575 A148576 A148577 * A148579 A148580 A148581

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved