A148405 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, 1, -1), (0, 0, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 5, 17, 51, 198, 687, 2836, 10749, 46067, 184597, 812310, 3381735, 15171550, 64957583, 295681089, 1293489193, 5954355415, 26493181563, 123052625899, 555024101601, 2596786703611, 11844164816717, 55752005243735, 256658725835629, 1214315074819775, 5633998302373761, 26772387983328833

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, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148403 A148404 A061675 * A216969 A148406 A148407

Adjacent sequences: A148402 A148403 A148404 * A148406 A148407 A148408

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved