A209867 a(n) = number of integers in range [2^(n-1),(2^n)-1] which permutation A209861/A209862 sends to odd-sized orbits.

1, 1, 2, 4, 6, 16, 12, 8, 14, 8, 406, 8, 56, 80, 1686, 8866, 8272, 15178, 9462, 938, 41128

Offset

0,3

Comments

a(0) gives the number of odd sized cycles in range [0,0], i.e. 1, as there is just one fixed point in that range.

Links

Table of n, a(n) for n=0..20.

Example

In range [2^(6-1),(2^6)-1] ([32,63]) of permutations A209861 & A209862, there are 6 cycles of size 1 (six fixed points), 2 cycles of size 3, one cycle of size 4, and 2 cycles of size 8, 6*1 + 2*3 + 1*4 + 2*8 = 32 in total, of which 6*1 + 2*3 elements are in odd-sized cycles, thus a(6)=12.

Crossrefs

a(n) = A000079(n-1) - A209868(n) for all n>0. Cf. A209860, A209863, A209864, A209865, A209866.

Sequence in context: A295615 A127679 A049022 * A136033 A343019 A355594

Adjacent sequences: A209864 A209865 A209866 * A209868 A209869 A209870

Keyword

nonn

Author

Antti Karttunen, Mar 24 2012

Status

approved