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A330620 Number of length n necklaces with entries covering an initial interval of positive integers and no adjacent entries equal. 2

%I #9 Jan 09 2020 19:36:43

%S 0,1,2,10,54,392,3378,34120,393738,5112406,73756026,1170482186,

%T 20263782630,380047964920,7676106365966,166114208828980,

%U 3834434324386350,94042629535109500,2442147034719168714,66942194906112161302,1931543452345335094678,58519191359163454708564

%N Number of length n necklaces with entries covering an initial interval of positive integers and no adjacent entries equal.

%H Andrew Howroyd, <a href="/A330620/b330620.txt">Table of n, a(n) for n = 1..200</a>

%e Case n=4: there are the following 10 necklaces:

%e 1212,

%e 1213, 1232, 1323,

%e 1234, 1243, 1324, 1342, 1423, 1432.

%o (PARI) \\ here U(n, k) is A208535(n, k) for n > 1.

%o U(n, k)={sumdiv(n, d, eulerphi(n/d)*(k-1)^d)/n - if(n%2, k-1)}

%o 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 Row sums of A330618.

%Y Cf. A019536, A208535.

%K nonn

%O 1,3

%A _Andrew Howroyd_, Dec 20 2019

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Last modified March 2 23:50 EST 2024. Contains 370499 sequences. (Running on oeis4.)