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%I #50 Sep 08 2022 08:44:43
%S 1,13,25,37,49,61,73,85,97,109,121,133,145,157,169,181,193,205,217,
%T 229,241,253,265,277,289,301,313,325,337,349,361,373,385,397,409,421,
%U 433,445,457,469,481,493,505,517,529,541,553,565,577,589,601,613,625,637
%N a(n) = 12*n + 1.
%H G. C. Greubel, <a href="/A017533/b017533.txt">Table of n, a(n) for n = 0..1000</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 12*n + 1, n >= 0.
%F a(n) = 24*n - 10 - a(n-1), (with a(0)=1). - _Vincenzo Librandi_, Dec 24 2010
%F G.f.: (1 + 11*x)/(1-x)^2. - _Indranil Ghosh_, Apr 05 2017
%F E.g.f.: (1 + 12*x)*exp(x). - _G. C. Greubel_, Sep 18 2019
%p seq(12*n+1, n=0..60); # _G. C. Greubel_, Sep 18 2019
%t Array[12*#+1&,60,0] (* _Vladimir Joseph Stephan Orlovsky_, Dec 14 2009 *)
%t CoefficientList[Series[(1+11x)/(1-x)^2, {x, 0,60}], x] (* _Michael De Vlieger_, Apr 05 2017 *)
%o (PARI) a(n)=12*n+1 \\ _Charles R Greathouse IV_, Jul 10 2016
%o (Python) def a(n): return 12*n + 1 # _Indranil Ghosh_, Apr 05 2017
%o (C)
%o #include<stdio.h>
%o int main(){
%o int n;
%o for(n=0; n<=100; n++)
%o printf("%d, ", 12*n + 1);
%o return 0;
%o } /* _Indranil Ghosh_, Apr 05 2017 */
%o (Magma) [12*n+1: n in [0..60]]; // _G. C. Greubel_, Sep 18 2019
%o (Sage) [12*n + 1 for n in (0..60)] # _G. C. Greubel_, Sep 18 2019
%o (GAP) List([0..60], n-> 12*n + 1); # _G. C. Greubel_, Sep 18 2019
%Y Cf. A161700, A005408, A016813, A016921, A017281, A158057, A161705, A161709, A161714, A128470, A016945, A287326 (third column).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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