A150310 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, 0), (1, 0, 1)}.

1, 2, 7, 21, 85, 294, 1281, 4784, 21615, 84503, 390514, 1574592, 7385698, 30449007, 144314993, 605050553, 2889602650, 12275638743, 58966155199, 253181758625, 1221674716683, 5291817489888, 25627253016512, 111831978695745, 543188151101798, 2385401611590782, 11614929999202359, 51286843298030434

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 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: A321283 A150308 A150309 * A150311 A150312 A150313

Adjacent sequences: A150307 A150308 A150309 * A150311 A150312 A150313

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved