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 A080981 #11 Jan 10 2024 16:35:07 %S A080981 0,2,10,12,44,50,52,178,180,204,210,216,228,716,722,728,740,818,820, %T A080981 844,866,868,872,914,920,932,2866,2868,2892,2914,2916,2920,2962,2968, %U A080981 2980,3276,3282,3288,3300,3378,3380,3468,3474,3480,3490,3492,3504,3528,3660 %N A080981 A014486-encodings of the trees whose interior zigzag-tree (Stanley's c) is branch-reduced (in the sense defined by Donaghey). %C A080981 Donaghey defines (on page 82 of his paper) the branch-reduced zigzag-trees as those zigzag-trees which do not contain longer than one-edge branches, where a branch is a maximal connected set of edges slanted to the same direction, with no perpendicular edges emanating from its middle. These form the primitive elements of the automorphism A057505/A057506. %H A080981 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 A080981 Antti Karttunen, <a href="/A014486/a014486.ps.gz">Initial terms illustrated in positions 0, 1, 2, 3, 5, 6, 7, 11, 12, 15, 16, 18, 20, 29, 30, 32, ...</a> %F A080981 a(n) = A014486(A080980(n)). %Y A080981 a(n) = A014486(A080980(n)). Cf. A080968, A080971. These trees are enumerated by A005554. %K A080981 nonn %O A080981 0,2 %A A080981 _Antti Karttunen_, Mar 02 2003