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 A365679 #22 Jul 28 2024 09:20:00
%S A365679 4,10,14,32,40,88,104,224,256,544,608,1280,1408,2944,3200,6656,7168,
%T A365679 14848,15872,32768,34816,71680,75776,155648,163840,335872,352256,
%U A365679 720896,753664,1540096,1605632,3276800,3407872,6946816,7208960,14680064
%N A365679 a(n) is the number of exterior top arches (no covering arch) for semi-meanders in generation n+1 that are generated by semi-meanders with n top arches and floor((n+2)/2) exterior top arches using the exterior arch splitting algorithm.
%C A365679 b(n) = the number of exterior top arches for all semi-meanders with n top arches and floor((n+2)/2) exterior top arches = (floor(n/2)+1) * 2^(floor((n-1)/2)). For n>=2, lim_{n->oo} a(n)/b(n) = 3.
%H A365679 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 4, 0, -4).
%F A365679 a(n) = (2*n-floor((n-1)/2)) * 2^floor((n-1)/2).
%e A365679 For n=4, the number of semi-meanders with 4 top arches and 3 exterior top arches is equal to A259689(4,3) = 2:
%e A365679 /\ /\
%e A365679 /\ /\ //\\, //\\ /\ /\ = 6 exterior arches. These 6 arches will generate 6 solutions in the n+1 generation using the exterior arch splitting algorithm.
%e A365679 _____ __ __ _____
%e A365679 / /\\ /\ //\\ _____ _____ //\\ /\ //\ \
%e A365679 /\ //\ //\\\, //\\ ///\\\, //\ /\\ /\ /\, /\ /\ //\ /\\, ///\\\ //\\, ///\\ /\\ /\
%e A365679 These 6 solutions have 14 exterior arches. Therefore a(4) = 14.
%t A365679 a[n_]:=(2*n-Floor[(n-1)/2]) * 2^Floor[(n-1)/2]; Array[a,36,2] (* _Stefano Spezia_, Sep 16 2023 *)
%Y A365679 Cf. A259689.
%K A365679 nonn
%O A365679 2,1
%A A365679 _Roger Ford_, Sep 15 2023
%E A365679 a(30) corrected by _Georg Fischer_, Jun 03 2024