A148372 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, 1, 1), (0, 1, 1), (1, -1, 0)}.

1, 1, 2, 5, 16, 42, 147, 456, 1632, 5436, 20292, 70488, 269689, 968663, 3772561, 13913269, 54903537, 206569753, 824553180, 3152717500, 12698822581, 49201218499, 199719855616, 782513292747, 3196926705307, 12644684394950, 51953020255292, 207173194254946, 855362862003040, 3435180546703850

Offset

0,3

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, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148369 A148370 A148371 * A148373 A132734 A148374

Adjacent sequences: A148369 A148370 A148371 * A148373 A148374 A148375

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved