A150218 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, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 6, 21, 82, 321, 1299, 5392, 22871, 98108, 424699, 1856216, 8183556, 36317895, 161980553, 725942682, 3268471012, 14774712211, 67005494929, 304779943331, 1390265877349, 6358331776667, 29145901592320, 133874784240042, 616114068765967, 2840641129896737, 13118766404752789, 60677043758756303

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, -1 + k, -1 + n] + aux[i, -1 + j, 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: A328434 A150216 A150217 * A150219 A150220 A168653

Adjacent sequences: A150215 A150216 A150217 * A150219 A150220 A150221

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved