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a(n) = 2*n^3 + 1.
9

%I #46 Aug 14 2023 16:20:34

%S 1,3,17,55,129,251,433,687,1025,1459,2001,2663,3457,4395,5489,6751,

%T 8193,9827,11665,13719,16001,18523,21297,24335,27649,31251,35153,

%U 39367,43905,48779,54001,59583,65537,71875,78609,85751,93313,101307,109745,118639,128001

%N a(n) = 2*n^3 + 1.

%C A058895(n)^3 + A068601(n)^3 + a(n)^3 = A185065(n)^3, for n>0. - _Vincenzo Librandi_, Mar 13 2012

%H Vincenzo Librandi, <a href="/A033562/b033562.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F G.f.: 1 + x*(3 + 5*x + 5*x^2 - x^3)/(1-x)^4. - _Vincenzo Librandi_, Mar 13 2012

%F E.g.f.: (1 + 2*x + 6*x^2 + 2*x^3)*exp(x). - _G. C. Greubel_, Oct 12 2019

%p seq(2*n^3+1, n=0..50); # _G. C. Greubel_, Oct 12 2019

%t 2*Range[0,50]^3+1 (* _Vladimir Joseph Stephan Orlovsky_, Feb 14 2011*)

%t CoefficientList[Series[1+x*(3+5x+5x^2-x^3)/(1-x)^4,{x,0,40}],x] (* _Vincenzo Librandi_, Mar 13 2012 *)

%t LinearRecurrence[{4,-6,4,-1},{1,3,17,55},50] (* _Harvey P. Dale_, Aug 14 2023 *)

%o (PARI) a(n)=2*n^3+1 \\ _Charles R Greathouse IV_, Mar 11 2012

%o (Magma) [2*n^3+1: n in [0..50]]; // _G. C. Greubel_, Oct 12 2019

%o (Sage) [2*n^3+1 for n in range(50)] # _G. C. Greubel_, Oct 12 2019

%o (GAP) List([0..50], n-> 2*n^3+1); # _G. C. Greubel_, Oct 12 2019

%Y Cf. A058895, A068601, A185065.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E Terms a(34) onward added by _G. C. Greubel_, Oct 12 2019