A148577 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, 0), (1, -1, 1), (1, 0, 0)}.

1, 1, 3, 6, 20, 50, 191, 541, 2177, 6673, 27348, 88173, 371217, 1243274, 5322458, 18365142, 79290736, 279861757, 1221272764, 4392018743, 19317981031, 70580799383, 311998052691, 1154903101359, 5134112863405, 19220501337271, 85835703816078, 324546760823938, 1454189667602518, 5545681979668163

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A138350 A148575 A148576 * A148578 A182299 A148579

Adjacent sequences: A148574 A148575 A148576 * A148578 A148579 A148580

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved