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A032283 "DIK" (bracelet, indistinct, unlabeled) transform of 2,2,2,2... 4
2, 5, 10, 21, 42, 95, 210, 510, 1258, 3249, 8538, 23033, 62778, 173451, 482690, 1353075, 3811362, 10785233, 30625194, 87239997, 249174234, 713416599, 2046945138, 5884580072, 16946835090, 48883925865, 141217957618, 408519816609, 1183291934298, 3431535849811 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

C. G. Bower, Transforms (2)

Index entries for sequences related to bracelets

FORMULA

G.f.: (x*(2+3*x-x^2)/((1-x)*(1-3*x^2)) + Sum_{d>0} phi(d)*log((1-x^d)/(1-3*x^d))/d)/2. - Andrew Howroyd, Jun 20 2018

MATHEMATICA

seq[n_] := (x*(2 + 3*x - x^2)/((1 - x)*(1 - 3*x^2)) + Sum[EulerPhi[d]*(Log[(1 - x^d)/(1 - 3*x^d)]/d), {d, 1, n}])/2 + O[x]^(n + 1) // CoefficientList[#, x]& // Rest;

seq[30] (* Jean-Fran├žois Alcover, Jul 02 2018, after Andrew Howroyd *)

PROG

(PARI) seq(n)={Vec(sum(d=1, n, eulerphi(d)/d*log((1-x^d)/(1-3*x^d) + O(x*x^n))) + x*(2+3*x-x^2)/((1-x)*(1-3*x^2)))/2} \\ Andrew Howroyd, Jun 20 2018

CROSSREFS

Sequence in context: A215410 A279668 A245747 * A266248 A027437 A267444

Adjacent sequences:  A032280 A032281 A032282 * A032284 A032285 A032286

KEYWORD

nonn

AUTHOR

Christian G. Bower

EXTENSIONS

Terms a(28) and beyond from Andrew Howroyd, Jun 20 2018

STATUS

approved

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Last modified October 22 04:04 EDT 2018. Contains 316431 sequences. (Running on oeis4.)