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Numbers that are congruent to {1, 6} mod 15.
3

%I #29 Dec 05 2018 20:18:02

%S 1,6,16,21,31,36,46,51,61,66,76,81,91,96,106,111,121,126,136,141,151,

%T 156,166,171,181,186,196,201,211,216,226,231,241,246,256,261,271,276,

%U 286,291,301,306,316,321,331,336,346,351,361,366,376,381,391,396,406

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

%C 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

%H Kival Ngaokrajang, <a href="/A087446/a087446.pdf">Illustration of initial terms</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1)

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

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

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

%F a(n) = 15*n - a(n-1) - 23, with a(1)=1. - _Vincenzo Librandi_, Aug 08 2010

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

%Y Cf. A001651, A047241, A087444, A087445.

%K nonn,easy

%O 1,2

%A _Paul Barry_, Sep 04 2003

%E Editing: rewording of Kival Ngaokrajang's comment. - _Wolfdieter Lang_, Dec 06 2014