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Number of 3-cycles in range [A014137(2n+2)..A014138(2n+2)] of permutation A057505 (= Donaghey's automorphism M).
4

%I #10 Jan 11 2024 02:51:47

%S 1,3,7,15,33,65,133,267

%N Number of 3-cycles in range [A014137(2n+2)..A014138(2n+2)] of permutation A057505 (= Donaghey's automorphism M).

%H Antti Karttunen, <a href="/A079442/a079442.pdf">Illustration of initial terms for trees of sizes 3..11</a>

%H Robert Donaghey, <a href="https://doi.org/10.1016/0095-8956(80)90045-3">Automorphisms on Catalan trees and bracketing</a>, J. Combin. Theory, Series B, 29 (1980), 75-90.

%F a(n) = A079442(2n+3)/3.

%Y Cf. A079440, A079442.

%K nonn,more

%O 0,2

%A _Antti Karttunen_, Jan 27 2003