A032285 "DIK" (bracelet, indistinct, unlabeled) transform of 4,4,4,4...

4, 14, 40, 125, 412, 1540, 6080, 25580, 111020, 494066, 2231960, 10201365, 47012620, 218126120, 1017565328, 4769086955, 22440958180, 105967383690, 501941663240, 2384203613501, 11353304737740, 54186129705260, 259150824770720, 1241763877376990, 5960465454101812

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.: (2*x*(2+5*x+x^2)/((1-x)*(1-5*x^2)) + Sum_{d>0} phi(d)*log((1-x^d)/(1-5*x^d))/d)/2. - Andrew Howroyd, Jun 20 2018

Prog

(PARI) seq(n)={Vec(2*x*(2+5*x+x^2)/((1-x)*(1-5*x^2)) + sum(d=1, n, eulerphi(d)/d*log((1-x^d)/(1-5*x^d) + O(x*x^n))))/2} \\ Andrew Howroyd, Jun 20 2018

Crossrefs

Cf. A032283.

Sequence in context: A072674 A202900 A238117 * A196451 A196480 A326008

Adjacent sequences: A032282 A032283 A032284 * A032286 A032287 A032288

Keyword

nonn

Author

Christian G. Bower

Extensions

Terms a(22) and beyond from Andrew Howroyd, Jun 20 2018

Status

approved