A149977 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), (0, 1, 0), (1, 0, 0), (1, 1, -1)}.

1, 2, 5, 16, 56, 214, 854, 3524, 14956, 64779, 285576, 1276474, 5772900, 26364344, 121406614, 563071754, 2627573408, 12327598936, 58109294319, 275054543064, 1306757230529, 6228761860551, 29777708624614, 142736752400576, 685842705210643, 3302635249425899, 15935263897361683, 77027482871983115

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, k, -1 + n] + aux[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: A149975 A149976 A141201 * A147771 A052891 A352905

Adjacent sequences: A149974 A149975 A149976 * A149978 A149979 A149980

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved