A150829 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), (0, 1, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 8, 32, 131, 584, 2603, 11787, 54485, 252720, 1184335, 5578698, 26422861, 125707588, 599883710, 2873578224, 13798398795, 66416805600, 320422819431, 1548598573276, 7497637554455, 36355592385793, 176533482570140, 858304434537674, 4177858821492626, 20358249251527439, 99300733157006749

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + 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, 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: A160637 A183895 A228921 * A155084 A322251 A150830

Adjacent sequences: A150826 A150827 A150828 * A150830 A150831 A150832

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved