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

Author

Paul Barry, Sep 04 2003

Keywords

• nonn
• easy

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

• Kival Ngaokrajang, Illustration of initial terms
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1)

Crossrefs

Cf. A001651, A047241, A087444, A087445.

Programs

Mathematica

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

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

Extensions

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