A150162 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, 0), (1, 0, -1), (1, 0, 1)}.

1, 2, 6, 20, 75, 284, 1137, 4644, 19393, 81898, 351374, 1520815, 6638275, 29196703, 129280300, 575406783, 2573623071, 11562972805, 52147022964, 235977654475, 1071303090569, 4877507991969, 22263040270667, 101860633661824, 467072841547863, 2145980198046295, 9878055487767915, 45548567570957663

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 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: A150159 A150160 A150161 * A150163 A150164 A150165

Adjacent sequences: A150159 A150160 A150161 * A150163 A150164 A150165

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved