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%I #15 Mar 30 2012 17:23:15
%S 0,0,0,0,2,0,20,56,114,248,106,1016,1992,4016,6506,7518,24496,50358,
%T 121610,261206,483160
%N a(n) = number of integers in range [2^(n-1),(2^n)-1] which permutation A209861/A209862 sends to even-sized orbits.
%C 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.
%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, 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.
%Y a(n) = A000079(n-1) - A209867(n) for all n>0. Cf. A209860, A209863, A209864, A209865, A209866.
%K nonn
%O 0,5
%A _Antti Karttunen_, Mar 24 2012
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