A150342 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, -1), (1, 0, -1), (1, 1, 0)}.

1, 2, 7, 23, 89, 338, 1379, 5614, 23661, 100182, 431677, 1872775, 8202961, 36172424, 160464569, 715888025, 3207758797, 14437490860, 65210961405, 295557019945, 1343597141551, 6124557345066, 27989276978537, 128197039382818, 588437982463403, 2706145730650444, 12467794226999059, 57537302320181571

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[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: A339038 A001338 A150341 * A124190 A176578 A150343

Adjacent sequences: A150339 A150340 A150341 * A150343 A150344 A150345

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved