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 A361378 #26 May 20 2023 16:17:26
%S A361378 0,1,2,3,3,3,8,8,12,16,25,33,45,66,91,128,177,252,351,491,689,966,
%T A361378 1354,1894,2658,3723,5217,7309,10244,14355,20112,28185,39494,55343,
%U A361378 77547,108667,152272,213372,298992,418968,587089,822665,1152777,1615350
%N A361378 Number of musical scales in n tone equal temperament respecting the property that alternate notes are 3 or 4 semitones apart.
%C A361378 If you take any three consecutive notes in the scales counted by a(n) (with cyclic identification) then the distance between the first and third is either 3 or 4 semitones. a(n) is also the number of subsets of Z/nZ that 1) contain 0; 2) contain no subset of the form {x,x+1,x+2}; 3) have no superset satisfying property 2).
%H A361378 Martin Epstein, <a href="https://mathstodon.xyz/@rivfader/109916586537191508">mastodon.xyz thread</a>, Feb 23 2023.
%H A361378 Donovan Young, <a href="/A361378/a361378.pdf">The number of scales with the natural thirds property</a>.
%H A361378 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1,0,-1).
%F A361378 a(n) = a(n-2) + a(n-3) + a(n-4) - a(n-6).
%F A361378 G.f.: x^2*(1+2*x+2*x^2-3*x^4)/(1-x^2-x^3-x^4+x^6).
%e A361378 For n=4 there are four notes, call them 0, 1, 2, and 3. The scales are 01, 02, and 03 and so a(4)=3.
%t A361378 LinearRecurrence[{0,1,1,1,0,-1},{0,1,2,3,3,3},100]
%K A361378 nonn,easy
%O A361378 1,3
%A A361378 _Donovan Young_, Mar 09 2023