A149943 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), (0, 1, -1), (0, 1, 0), (1, 0, -1), (1, 1, 0)}

1, 2, 5, 15, 49, 172, 627, 2374, 9218, 36536, 147576, 604114, 2505636, 10503384, 44429132, 189530129, 814217984, 3520596956, 15311050911, 66930619301, 293971727765, 1296689732244, 5742062449808, 25518877148421, 113785729926120, 508913759962817, 2282592025746653, 10264924766267955

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, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + 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: A149940 A149941 A149942 * A079146 A000734 A148366

Adjacent sequences: A149940 A149941 A149942 * A149944 A149945 A149946

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved