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%I #27 Sep 08 2022 08:45:49
%S 0,1,5,21,37,53,69,85,101,117,133,149,165,181,197,213,229,245,261,277,
%T 293,309,325,341,357,373,389,405,421,437,453,469,485,501,517,533,549,
%U 565,581,597,613,629,645,661,677,693,709,725,741,757,773,789,805
%N a(0)=0, a(1)=1 and a(n) = 16n-27 for n >= 2.
%H Vincenzo Librandi, <a href="/A170837/b170837.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 G.f.: x*(3*x+12*x^2+1)/(x-1)^2.
%F a(n) = 2*a(n-1) -a(n-2), n>=4.
%F a(n) = 4*A016813(n-2) + 1, n>=2. - _Ivan N. Ianakiev_, Jul 20 2013
%t CoefficientList[Series[x*(3*x + 12*x^2 + 1)/(x - 1)^2, {x, 0, 60}], x] (* _Vincenzo Librandi_, Dec 19 2012 *)
%t LinearRecurrence[{2,-1},{0,1,5,21},60] (* _Harvey P. Dale_, Oct 09 2017 *)
%o (Magma) I:=[0, 1, 5, 21]; [n le 4 select I[n] else 2*Self(n-1) - Self(n-2): n in [1..60]]; // _Vincenzo Librandi_, Dec 19 2012
%Y Cf. A170836 (first differences), A170876.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Jan 05 2010, based on email from _R. J. Mathar_ and _Benoit Jubin_, Jun 02 2009; revised Jan 09 2010
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