cp's OEIS Frontend

A169724 (2*3^(n-1)+1)^2.

%I A169724 #18 Apr 23 2024 11:04:05
%S A169724 9,49,361,3025,26569,237169,2128681,19140625,172213129,1549760689,
%T A169724 13947373801,125524947025,1129720271689,10167469690609,91507188951721,
%U A169724 823564585774225,7412080927594249,66708727315226929,600378542737678441,5403406875341014225
%N A169724 (2*3^(n-1)+1)^2.
%C A169724 A subsequence of the squares A000290.
%C A169724 Essentially equal to A052919(n)^2.
%H A169724 Vincenzo Librandi, <a href="/A169724/b169724.txt">Table of n, a(n) for n = 1..1000</a>
%H A169724 Alice V. Kleeva, <a href="/A169724/a169724a.jpg">Grid for this sequence</a>
%H A169724 Alice V. Kleeva, <a href="/A169724/a169724b.jpg">Illustration of initial terms</a>
%H A169724 Robert Munafo, <a href="http://www.mrob.com/pub/math/seq-a169720.html">Sequence A169720, and two others by Alice V. Kleeva</a>
%H A169724 Robert Munafo, <a href="/A169720/a169720.pdf">Sequence A169720, and two others by Alice V. Kleeva</a> [Cached copy, in pdf format, included with permission]
%H A169724 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (13,-39,27).
%F A169724 a(n)= +13*a(n-1) -39*a(n-2) +27*a(n-3). G.f.: x*( -9+68*x-75*x^2 ) / ( (x-1)*(3*x-1)*(9*x-1) ). [_R. J. Mathar_, Apr 26 2010]
%t A169724 CoefficientList[Series[(-9 + 68 x - 75 x^2)/((x - 1) (3 x - 1) (9 x - 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 03 2012 *)
%t A169724 LinearRecurrence[{13,-39,27},{9,49,361},20] (* _Harvey P. Dale_, Apr 23 2024 *)
%o A169724 (Magma) I:=[9, 49, 361]; [n le 3 select I[n] else 13*Self(n-1) - 39*Self(n-2) + 27*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Dec 03 2012
%Y A169724 Cf. A169720-A169727, A100702.
%K A169724 nonn,easy
%O A169724 1,1
%A A169724 Alice V. Kleeva (alice27353(AT)gmail.com), Jan 19 2010
%E A169724 G.f. adapted to the offset by _Vincenzo Librandi_, Dec 03 2012