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

Author

Antti Karttunen, Mar 24 2012

Keywords

• nonn

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.

Examples

			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.