1,2

3*a(n) is conjectured to be the number of edges (bonds) visited when walking around the boundary of a certain equilateral triangle construction at the n-th iteration. See the illustration in the link. Note that isthmus edges (bridges) are counted twice. The pattern is supposed to become the planar Archimedean net 3.12.12 when n -> infinity. - Kival Ngaokrajang, Nov 30 2014

Kival Ngaokrajang, Illustration of initial terms

Index entries for linear recurrences with constant coefficients, signature (1,1,-1)

G.f.: x*(1 + 5*x + 9*x^2)/((1 + x)*(1 - x)^2).

E.g.f.: (30*x-1)*exp(x)/4 + 5*exp(-x)/4.

a(n) = (18*n-1)/4 + 5*(-1)^n/4.

a(n) = 15*n - a(n-1) - 23, with a(1)=1. - Vincenzo Librandi, Aug 08 2010

#+{1, 6}&/@(15*Range[0, 30])//Flatten (* or *) LinearRecurrence[{1, 1, -1}, {1, 6, 16}, 60] (* Harvey P. Dale, Dec 05 2018 *)

Cf. A001651, A047241, A087444, A087445.

Sequence in context: A291746 A037001 A118139 * A340497 A051808 A034053

Adjacent sequences: A087443 A087444 A087445 * A087447 A087448 A087449

nonn,easy

Paul Barry, Sep 04 2003

Editing: rewording of Kival Ngaokrajang's comment. - Wolfdieter Lang, Dec 06 2014

approved