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Python 2, 39 bytes f=lambda n:n>9and 10*f(n/10)or 5>>5/-~n Try it online!

Python 2, 24 bytes lambda n:2-(-n%n**.5<.5) Try it online! Outputs the \$n\$'th value one-indexed. We use an arithmetic expression to identify indices n that are either perfect square or one below a …

Haskell, 31 bytes do n<-[1..];show$div(100^n)9*11 Try it online! 32 bytes show=<<iterate(\x->x*100+121)121 Try it online!

Python 3, crashoz, 45 bytes lambda n:int(60*math.sin(n/10-2)) import math Try it online! The expression x*60-x**3*10+x**5/2-x**7/84 is the Taylor series for \$\sin(x)\$ up to the \$x^7\$ term, multi …

Haskell, 25 bytes (iterate(\m->m*m-m+1)2!!)

Haskell, 67 bytes 0%j=2 i%j|d<-div i$f j=last$d+2:[(i-d-1)%(j+1)|d*f j<i] f=(%1).pred Try it online! A recursive arithmetical solution that turned out basically the same method as Anders Kaseorg …

Python 2, 101 bytes n=input() for i in range(2**n):s='';m=n;exec"s=`m`+'+-'[i%2]+s;s*='-'in s;i/=2;m-=1;"*m;print s or'-' Try it online!

Python 2, 46 bytes lambda n:map(range(1,n+1).pop,n/4*[-1,0,0,-1]) Try it online! Generates the range [1..n] and pops from the front and back in the repeating pattern back, front, front, back, .. …

Haskell, 45 bytes f l=max[[]][h:y|h:t<-l,y<-f$t:filter(/=h:t)l] Try it online! Adapted from Chas Brown's Python answer. The max[[]] is a trick to give a base case of [[]] when the input only c …

Haskell, 44 bytes g.(*3).max 1 g 0=0 g n=0^mod n 3+g(div n 10) Try it online! Uses Delfad0r's observation that the output is the number of suffixes (equivalently, prefixes) of 3n that are multip …

Python 2, 48 bytes n=input()*3;p=n<1 while n:p+=n%3<1;n/=10 print p Try it online! Similar to ovs's answer, but takes the whole prefix mod 3 without accumulating rather than the last digit. Outp …

Haskell, 55 bytes (1%[0]!!) a%o|b<-div a 2=a:last(b:[3*a|elem b o])%(a:o) Try it online! Golfing user1472751's slick list-generation method. Same length: (1%[0]!!) a%o=a:[x|x<-[div a 2,a*3], …

Haskell, 50 bytes f n=[l|k<-[0..],l<-mapM([0..k]<$f)[0..n],sum l==k] Try it online! Lists n-tuples sorted by sum. mapM does the heavy lifting to generate all n-tuples of numbers from 0 to k. The …

It turns out shorter to generate 2**n minus each term in the sequence for input n. …

Uses a version of Bubbler's observation that the sequence alternates runs of consecutive odd numbers with an even number directly in between. …