A150570 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, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 26, 108, 453, 1967, 8706, 39090, 177790, 816687, 3781530, 17611689, 82495489, 388239450, 1834554841, 8700456703, 41396000957, 197502228696, 944598518988, 4527944745628, 21748772881792, 104656528669946, 504467991736809, 2435414066188900, 11773906700835303, 56994025754728403, 276223254953266320

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[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: A124542 A003447 A150569 * A150571 A150572 A150573

Adjacent sequences: A150567 A150568 A150569 * A150571 A150572 A150573

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved