A154609 - OEIS

%I #27 May 31 2024 05:47:29

%S 5,18,31,44,57,70,83,96,109,122,135,148,161,174,187,200,213,226,239,

%T 252,265,278,291,304,317,330,343,356,369,382,395,408,421,434,447,460,

%U 473,486,499,512,525,538,551,564,577,590,603,616,629,642,655,668,681,694

%N a(n) = 13*n + 5.

%C Any square mod 13 is one of 0, 1, 3, 4, 9, 10 or 12 (A010376) but not 5, for this reason there are no squares in sequence. - _Bruno Berselli_, Feb 19 2016

%H Vincenzo Librandi, <a href="/A154609/b154609.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F From _Vincenzo Librandi_, Feb 26 2012: (Start)

%F G.f.: (5+8*x)/(1-x)^2.

%F a(n) = 2*a(n-1) - a(n-2). (End)

%F E.g.f.: (5 + 13*x)*exp(x). - _G. C. Greubel_, May 31 2024

%t Range[5, 1000, 13] (* _Vladimir Joseph Stephan Orlovsky_, May 31 2011 *)

%t CoefficientList[Series[(8 x + 5)/(1 - x)^2, {x, 0, 60}], x] (* _Vincenzo Librandi_, Feb 26 2012 *)

%o (PARI) a(n)=13*n+5 \\ _Charles R Greathouse IV_, Dec 28 2011

%o (Magma) I:=[5, 18]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 26 2012

%o (SageMath) [13*n+5 for n in range(61)] # _G. C. Greubel_, May 31 2024

%Y Cf. A010376,

%Y Sequences of the form 13*n+q: A008595 (q=0), A190991 (q=1), A153080 (q=2), A127547 (q=4), this sequence (q=5), A186113 (q=6), A269044 (q=7), A269100 (q=11).

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Jan 15 2009