A150484 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), (0, 0, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 25, 100, 409, 1706, 7266, 31440, 137453, 606406, 2694978, 12050761, 54172483, 244631445, 1109052334, 5045467997, 23024221298, 105354826753, 483273587306, 2221770279348, 10234883222231, 47235417223485, 218367202628453, 1011074661721865, 4688174335901862, 21767247807322779, 101190992430093135

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A150481 A150482 A150483 * A150485 A150486 A150487

Adjacent sequences: A150481 A150482 A150483 * A150485 A150486 A150487

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved