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Number of cycles of length n under the mapping x -> x^2-2 modulo Fermat prime 2^(2^m)+1, where m is any fixed integer such that n divides 2^m-1.
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%I #18 Jun 22 2024 16:15:53

%S 1,1,3,9,28,93,315,1091,3855,13797,49929,182361,671088,2485504,

%T 9256395,34636833,130150493,490853403,1857283155,7048151355,

%U 26817356775,102280151421,390937467284,1497207322929,5744387279808,22076468760335

%N Number of cycles of length n under the mapping x -> x^2-2 modulo Fermat prime 2^(2^m)+1, where m is any fixed integer such that n divides 2^m-1.

%C Halved bisection of A001037.

%C Bisection of A000048. Number of 2m bead balanced binary necklaces of fundamental period 4n+2 that are equivalent to their complements, where m is any multiple of 2n+1. - _Aaron Meyerowitz_, Jun 01 2024

%F a(n) = A001037(2n+1)/2.

%Y Cf. A000048, A001037, A059966.

%K nonn

%O 0,3

%A _Max Alekseyev_, Sep 27 2007