A087446 Numbers that are congruent to {1, 6} mod 15.

1, 6, 16, 21, 31, 36, 46, 51, 61, 66, 76, 81, 91, 96, 106, 111, 121, 126, 136, 141, 151, 156, 166, 171, 181, 186, 196, 201, 211, 216, 226, 231, 241, 246, 256, 261, 271, 276, 286, 291, 301, 306, 316, 321, 331, 336, 346, 351, 361, 366, 376, 381, 391, 396, 406

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..55.

Kival Ngaokrajang, Illustration of initial terms

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

Formula

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

Mathematica

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

Crossrefs

Cf. A001651, A047241, A087444, A087445.

Sequence in context: A291746 A037001 A118139 * A340497 A051808 A034053

Adjacent sequences: A087443 A087444 A087445 * A087447 A087448 A087449

Keyword

nonn,easy

Author

Paul Barry, Sep 04 2003

Extensions

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

Status

approved