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a(n) = 18*n + 1.
19

%I #46 Sep 08 2022 08:45:45

%S 1,19,37,55,73,91,109,127,145,163,181,199,217,235,253,271,289,307,325,

%T 343,361,379,397,415,433,451,469,487,505,523,541,559,577,595,613,631,

%U 649,667,685,703,721,739,757,775,793,811,829,847,865,883,901,919,937,955

%N a(n) = 18*n + 1.

%C Digital root of a(n) is 1. - _Alexander R. Povolotsky_, Jun 13 2012

%C 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 G. C. Greubel, <a href="/A161705/b161705.txt">Table of n, a(n) for n = 0..2500</a>

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

%F a(n) = 18*n + 1, n >= 0.

%F a(n) = a(n-1) + 18 (with a(0)=1). - _Vincenzo Librandi_, Dec 27 2010

%F From _G. C. Greubel_, Feb 17 2017: (Start)

%F G.f.: (1 + 17*x)/(1-x)^2.

%F E.g.f.: (1 + 18*x)*exp(x).

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

%p seq(18*n+1, n=0..60); # _G. C. Greubel_, Sep 18 2019

%t Range[1, 1000, 18] (* _Vladimir Joseph Stephan Orlovsky_, Jun 01 2011 *)

%t LinearRecurrence[{2,-1},{1,19}, 60] (* _G. C. Greubel_, Feb 17 2017 *)

%o (PARI) vector(60, n, 18*n-17) \\ _G. C. Greubel_, Feb 17 2017

%o (Magma) [18*n +1: n in [0..60]]; // _G. C. Greubel_, Sep 18 2019

%o (Sage) [18*n+1 for n in (0..60)] # _G. C. Greubel_, Sep 18 2019

%o (GAP) List([0..60], n-> 18*n+1); # _G. C. Greubel_, Sep 18 2019

%Y Cf. A005408, A016813, A016921, A017281, A017533, A128470, A158057, A161700, A161709, A161714, A287326 (fourth column).

%K nonn,easy

%O 0,2

%A _Reinhard Zumkeller_, Jun 17 2009