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%I #18 Mar 04 2024 01:12:23
%S 5,15,15,25,25,35,35,45,45,55,55,65,65,75,75,85,85,95,95,105,105,115,
%T 115,125,125,135,135,145,145,155,155,165,165,175,175,185,185,195,195,
%U 205,205,215,215,225,225,235,235,245,245,255,255,265,265,275,275,285
%N a(n) = 10*n - a(n-1), with n>1, a(1)=5.
%H Vincenzo Librandi, <a href="/A166621/b166621.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F From _Vincenzo Librandi_, Sep 15 2013: (Start)
%F G.f.: -x*(-5-10*x+5*x^2)/((1+x)*(x-1)^2).
%F a(n) = a(n-1) + a(n-2) - a(n-3). (End)
%F E.g.f.: 5*((1+x)*cosh(x) + x*sinh(x) - 1). - _G. C. Greubel_, May 18 2016
%t RecurrenceTable[{a[1]==5, a[n]==10n-a[n-1]}, a, {n, 60}] (* or *) CoefficientList[Series[-(- 5 - 10 x + 5 x^2) /((1 + x) (x - 1)^2), {x, 0, 60}], x] (* _Vincenzo Librandi_, Sep 15 2013 *)
%o (Magma) [n le 1 select (n+4) else 10*n-Self(n-1): n in [1..70] ]; // _Vincenzo Librandi_, Sep 15 2013
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Oct 18 2009
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