A149813 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, 0), (-1, 1, -1), (0, 0, 1), (1, 0, 0)}.

1, 2, 4, 10, 26, 71, 229, 744, 2409, 8124, 27190, 93997, 339021, 1214115, 4385648, 15983458, 58302056, 217544034, 820036649, 3084534154, 11674973196, 44268101746, 168984174425, 652759187170, 2525763157524, 9782225262491, 37993427103799, 147899104605241, 579728181733964, 2283629130688732

Offset

0,2

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A106221 A149811 A149812 * A149814 A125108 A075864

Adjacent sequences: A149810 A149811 A149812 * A149814 A149815 A149816

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved