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

Author

Antti Karttunen, Mar 24 2012

Keywords

• nonn

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.

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, 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.