A209868 a(n) = number of integers in range [2^(n-1),(2^n)-1] which permutation A209861/A209862 sends to even-sized orbits.

0, 0, 0, 0, 2, 0, 20, 56, 114, 248, 106, 1016, 1992, 4016, 6506, 7518, 24496, 50358, 121610, 261206, 483160

Offset

0,5

Comments

a(0) gives the number of even-sized cycles in range [0,0], i.e. 0, as there is only 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, i.e. 6*1 + 2*3 + 1*4 + 2*8 = 32 in total, of which 4 + 2*8 elements are in even-sized cycles, thus a(6)=20.

Crossrefs

a(n) = A000079(n-1) - A209867(n) for all n>0. Cf. A209860, A209863, A209864, A209865, A209866.

Sequence in context: A280622 A211880 A365862 * A182661 A189772 A217311

Adjacent sequences: A209865 A209866 A209867 * A209869 A209870 A209871

Keyword

nonn

Author

Antti Karttunen, Mar 24 2012

Status

approved