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 A381936 #31 Mar 19 2025 09:03:09
%S A381936 0,1,1,1,3,3,8,11,20,30,55,83,144,224,373,597,987,1572,2584,4146,6756,
%T A381936 10890,17711,28557,46365,74880,121372,196184,317811,513818,832040,
%U A381936 1345659,2178253,3523590,5702876,9225784,14930352,24155232,39088024,63241794,102334155,165573148,267914296
%N A381936 Number of primitive binary words of length n that avoid 11, start with 1 and end with 0.
%C A381936 Here primitive means the word is not two or more repetitions of a smaller word.
%F A381936 a(n) = Sum_{d|n} mu(d) * Fibonacci(n/d-1).
%e A381936 For n=5, the a(6) = 3 words are: 100000, 100010, 101000.
%e A381936 Notice 100100 is not included since it is repetitions of the smaller word 100 (from n=3).
%o A381936 (PARI) a(n) = sumdiv(n,d,moebius(d)*fibonacci(n/d-1)) \\ _Andrew Howroyd_, Mar 10 2025
%o A381936 (Python)
%o A381936 from sympy import mobius, fibonacci, divisors
%o A381936 def A381936(n): return sum(mobius(n//d)*fibonacci(d-1) for d in divisors(n,generator=True)) # _Chai Wah Wu_, Mar 18 2025
%Y A381936 Cf. A000045, A007436, A008683, A056267, A113166.
%K A381936 nonn
%O A381936 1,5
%A A381936 _Aidan Diekmann_, Mar 10 2025