A032283 "DIK" (bracelet, indistinct, unlabeled) transform of 2,2,2,2...

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

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-François 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: A279668 A352875 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