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A106366 Necklaces with n beads of 4 colors, no 2 adjacent beads the same color. 3
4, 6, 8, 24, 48, 130, 312, 834, 2192, 5934, 16104, 44368, 122640, 341802, 956632, 2690844, 7596480, 21524542, 61171656, 174342216, 498112272, 1426419858, 4093181688, 11767920118, 33891544416, 97764131646, 282429537944 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

Index entries for sequences related to necklaces

FORMULA

CycleBG transform of (4, 0, 0, 0, ...)

CycleBG transform T(A) = invMOEBIUS(invEULER(Carlitz(A)) + A(x^2) - A) + A.

Carlitz transform T(A(x)) has g.f. 1/(1-Sum_{k>0} (-1)^(k+1)*A(x^k)).

a(n) = (1/n) * Sum_{d | n} totient(n/d) * (3*(-1)^d + 3^d) for n > 1. - Andrew Howroyd, Mar 12 2017

MATHEMATICA

a[n_] := If[n==1, 4, Sum[EulerPhi[n/d]*(3*(-1)^d+3^d), {d, Divisors[n]}]/n ];

Array[a, 35] (* Jean-François Alcover, Jul 06 2018, after Andrew Howroyd *)

PROG

(PARI) a(n) = if(n==1, 4, sumdiv(n, d, eulerphi(n/d)*(3*(-1)^d + 3^d))/n); \\ Andrew Howroyd, Oct 14 2017

CROSSREFS

Column 4 of A208535.

Cf. A000031, A001868, A226493.

Sequence in context: A074125 A063719 A272862 * A019160 A126233 A059889

Adjacent sequences:  A106363 A106364 A106365 * A106367 A106368 A106369

KEYWORD

nonn

AUTHOR

Christian G. Bower, Apr 29 2005

STATUS

approved

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Last modified January 24 04:35 EST 2020. Contains 331183 sequences. (Running on oeis4.)