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%I #13 Mar 30 2012 17:23:15
%S 1,1,2,4,6,16,12,8,14,8,406,8,56,80,1686,8866,8272,15178,9462,938,
%T 41128
%N a(n) = number of integers in range [2^(n-1),(2^n)-1] which permutation A209861/A209862 sends to odd-sized orbits.
%C 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.
%e 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.
%Y a(n) = A000079(n-1) - A209868(n) for all n>0. Cf. A209860, A209863, A209864, A209865, A209866.
%K nonn
%O 0,3
%A _Antti Karttunen_, Mar 24 2012
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