cp's OEIS Frontend

A161705 a(n) = 18*n + 1.

%I A161705 #49 Apr 12 2025 13:06:47
%S A161705 1,19,37,55,73,91,109,127,145,163,181,199,217,235,253,271,289,307,325,
%T A161705 343,361,379,397,415,433,451,469,487,505,523,541,559,577,595,613,631,
%U A161705 649,667,685,703,721,739,757,775,793,811,829,847,865,883,901,919,937,955
%N A161705 a(n) = 18*n + 1.
%C A161705 Digital root of a(n) is 1. - _Alexander R. Povolotsky_, Jun 13 2012
%C A161705 These numbers can be written as the sum of four integer cubes as a(n) = (2*n + 14)^3 + (3*n + 30)^3 + (- 2*n - 23)^3 + (- 3*n - 26)^3. - _Arkadiusz Wesolowski_, Aug 15 2013
%H A161705 G. C. Greubel, <a href="/A161705/b161705.txt">Table of n, a(n) for n = 0..2500</a>
%H A161705 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A161705 a(n) = 18*n + 1, n >= 0.
%F A161705 a(n) = a(n-1) + 18 (with a(0)=1). - _Vincenzo Librandi_, Dec 27 2010
%F A161705 From _G. C. Greubel_, Feb 17 2017: (Start)
%F A161705 G.f.: (1 + 17*x)/(1-x)^2.
%F A161705 E.g.f.: (1 + 18*x)*exp(x).
%F A161705 a(n) = 2*a(n-1) - a(n-2). (End)
%F A161705 a(n) = A017173(2*n) = A016777(6*n). - _Elmo R. Oliveira_, Apr 12 2025
%p A161705 seq(18*n+1, n=0..60); # _G. C. Greubel_, Sep 18 2019
%t A161705 Range[1, 1000, 18] (* _Vladimir Joseph Stephan Orlovsky_, Jun 01 2011 *)
%t A161705 LinearRecurrence[{2,-1},{1,19}, 60] (* _G. C. Greubel_, Feb 17 2017 *)
%o A161705 (PARI) vector(60, n, 18*n-17) \\ _G. C. Greubel_, Feb 17 2017
%o A161705 (Magma) [18*n +1: n in [0..60]]; // _G. C. Greubel_, Sep 18 2019
%o A161705 (Sage) [18*n+1 for n in (0..60)] # _G. C. Greubel_, Sep 18 2019
%o A161705 (GAP) List([0..60], n-> 18*n+1); # _G. C. Greubel_, Sep 18 2019
%Y A161705 Cf. A005408, A016813, A016921, A017281, A017533, A128470, A158057, A161700, A161709, A161714, A287326 (fourth column).
%Y A161705 Cf. A016777, A017173.
%K A161705 nonn,easy
%O A161705 0,2
%A A161705 _Reinhard Zumkeller_, Jun 17 2009