A148051 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), (-1, -1, 1), (-1, 0, -1), (-1, 1, 0), (1, 0, 0)}.

1, 1, 2, 3, 10, 20, 63, 133, 488, 1134, 4159, 9977, 38619, 96551, 380001, 972913, 3913896, 10241310, 41846263, 111378893, 461040755, 1244667953, 5208010325, 14229194099, 60121447699, 165980137990, 706675809803, 1968160352808, 8441479695283, 23696553049202, 102251059507356, 289003009054919, 1253963610330642

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A148048 A148049 A148050 * A148052 A148053 A148054

Adjacent sequences: A148048 A148049 A148050 * A148052 A148053 A148054

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved