A148906 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, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 32, 105, 429, 1563, 6673, 25959, 112651, 457235, 2015671, 8422815, 37516109, 160145249, 719358925, 3120482258, 14110389142, 61984334190, 281826273716, 1250535422363, 5711981682731, 25554828817066, 117181130626924, 527847897054903, 2428588448829353, 11002765062169712, 50771524681148388

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + 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: A148904 A218882 A148905 * A148907 A148908 A148909

Adjacent sequences: A148903 A148904 A148905 * A148907 A148908 A148909

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved