cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A154267 a(n) = 27*n + 15.

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%I A154267 #45 Sep 08 2022 08:45:40
%S A154267 15,42,69,96,123,150,177,204,231,258,285,312,339,366,393,420,447,474,
%T A154267 501,528,555,582,609,636,663,690,717,744,771,798,825,852,879,906,933,
%U A154267 960,987,1014,1041,1068,1095,1122,1149,1176,1203,1230,1257,1284,1311,1338
%N A154267 a(n) = 27*n + 15.
%C A154267 The identity (81*n^2 + 90*n + 26)^2 - (9*n^2 + 10*n + 3)*(27*n + 15)^2 = 1 can be written as A154277(n+1)^2 - A154254(n+1)*a(n)^2 = 1. - _Vincenzo Librandi_, Feb 03 2012
%H A154267 Vincenzo Librandi, <a href="/A154267/b154267.txt">Table of n, a(n) for n = 0..10000</a>
%H A154267 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A154267 G.f.: 3*(5 + 4*x)/(1-x)^2. - _R. J. Mathar_, Jan 05 2011
%F A154267 a(n) = 3*A017221(n). - _R. J. Mathar_, Jan 05 2011
%F A154267 a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Feb 02 2012
%F A154267 E.g.f.: (27*x + 15)*exp(x). - _G. C. Greubel_, Sep 08 2016
%t A154267 Range[15, 7000, 27] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *)
%t A154267 LinearRecurrence[{2, -1}, {15, 42}, 40] (* _Vincenzo Librandi_, Feb 02 2012 *)
%t A154267 27*Range[0,50]+15 (* _Harvey P. Dale_, Feb 26 2017 *)
%o A154267 (PARI) a(n)=27*n+15 \\ _Charles R Greathouse IV_, Dec 28 2011
%o A154267 (Magma) I:=[15, 42]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 02 2012
%Y A154267 Cf. A154254, A154277.
%K A154267 nonn,easy
%O A154267 0,1
%A A154267 _Vincenzo Librandi_, Jan 06 2009