A151088 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), (0, 0, 1), (0, 1, -1), (1, 0, 0), (1, 0, 1)}.

1, 3, 11, 42, 172, 731, 3190, 14185, 64088, 293148, 1353721, 6301445, 29532269, 139193588, 659208293, 3135042374, 14964198986, 71655310992, 344084815185, 1656435921209, 7992078959506, 38638407637592, 187140937165574, 907895549056257, 4411184925380861, 21461987349753724, 104551592003011526

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A200030 A084782 A149068 * A149069 A151089 A211854

Adjacent sequences: A151085 A151086 A151087 * A151089 A151090 A151091

Keyword

nonn,walk,changed

Author

Manuel Kauers, Nov 18 2008

Status

approved