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%I #9 Jan 10 2024 16:34:41
%S 0,0,1,1,1,2,2,2,3,3,3,4,4,4,6,6,6,7,8,8,9,9,11,12,12,12,14,14,14,15,
%T 17,17,18,18,19,20,20,20,23,23,23,24,25,25,26,26,28,29,29,29,31,31,31,
%U 32,34,34,35,35,36,37,37,37,40,40,40,41,42,42,43,43,45,46,46,46,48,48,48
%N Number of transpositions (2-cycles) in range [A014137(n-1)..A014138(n-1)] of permutation A057505 (= Donaghey's automorphism M).
%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.
%H Antti Karttunen, <a href="/A079438/a079438.pdf">Illustration of initial terms for trees of sizes n=2..18</a>
%p A079440 := n -> floor((n+1)/3) + `if`((n>=14),floor((n-10)/4)+floor((n-14)/8),0);
%Y From n>= 2 onward a(n) = A079438(n)/2 (with the same reservation). Cf. A079444.
%K nonn
%O 0,6
%A _Antti Karttunen_, Jan 27 2003