cp's OEIS Frontend

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.

A330621 Number of length n bracelets with entries covering an initial interval of positive integers and no adjacent entries equal.

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%I A330621 #9 Jan 09 2020 19:28:44
%S A330621 0,1,1,7,27,207,1689,17137,196869,2556856,36878013,585247590,
%T A330621 10131891315,190024056601,3838053182983,83057105368627,
%U A330621 1917217162193175,47021314781221603,1221073517359584357,33471097453271690668,965771726172667547339,29259595679585441629303
%N A330621 Number of length n bracelets with entries covering an initial interval of positive integers and no adjacent entries equal.
%H A330621 Andrew Howroyd, <a href="/A330621/b330621.txt">Table of n, a(n) for n = 1..200</a>
%e A330621 Case n=4: there are the following 7 bracelets:
%e A330621   1212,
%e A330621   1213, 1232, 1323,
%e A330621   1234, 1243, 1324.
%o A330621 (PARI) \\ here U(n, k) is A208544(n, k) for n > 1.
%o A330621 U(n, k) = (sumdiv(n, d, eulerphi(n/d)*(k-1)^d)/n + if(n%2, 1-k, k*(k-1)^(n/2)/2))/2;
%o A330621 a(n)={if(n<1, n==0, sum(j=1, n, U(n,j)*sum(k=j, n, (-1)^(k-j)*binomial(k, j))))}
%Y A330621 Row sums of A330341.
%Y A330621 Cf. A208544.
%K A330621 nonn
%O A330621 1,4
%A A330621 _Andrew Howroyd_, Dec 20 2019