This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A079440 #9 Jan 10 2024 16:34:41 %S A079440 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 A079440 17,17,18,18,19,20,20,20,23,23,23,24,25,25,26,26,28,29,29,29,31,31,31, %U A079440 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 A079440 Number of transpositions (2-cycles) in range [A014137(n-1)..A014138(n-1)] of permutation A057505 (= Donaghey's automorphism M). %H A079440 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 A079440 Antti Karttunen, <a href="/A079438/a079438.pdf">Illustration of initial terms for trees of sizes n=2..18</a> %p A079440 A079440 := n -> floor((n+1)/3) + `if`((n>=14),floor((n-10)/4)+floor((n-14)/8),0); %Y A079440 From n>= 2 onward a(n) = A079438(n)/2 (with the same reservation). Cf. A079444. %K A079440 nonn %O A079440 0,6 %A A079440 _Antti Karttunen_, Jan 27 2003