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%I #27 Sep 08 2022 08:45:10
%S 5,5,10,20,35,55,80,110,145,185,230,280,335,395,460,530,605,685,770,
%T 860,955,1055,1160,1270,1385,1505,1630,1760,1895,2035,2180,2330,2485,
%U 2645,2810,2980,3155,3335,3520,3710,3905,4105,4310,4520,4735,4955,5180,5410,5645
%N a(n) = 5*(n^2-n+2)/2.
%C Also the sum of five consecutive triangular numbers starting with A000217(-3). - _Bruno Berselli_, Jun 18 2015
%D Found on a quiz.
%H Harvey P. Dale, <a href="/A082450/b082450.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 5*n + a(n-1)-5 for n>0, a(0)=5. - _Vincenzo Librandi_, Aug 08 2010
%F a(0)=5, a(1)=5, a(2)=10; for n>2, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - _Harvey P. Dale_, Mar 23 2013
%F G.f.: 5*(1-2*x+2*x^2)/(1-x)^3. - _Wesley Ivan Hurt_, May 02 2021
%t Table[(5(n^2-n+2))/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{5,5,10},50] (* _Harvey P. Dale_, Mar 23 2013 *)
%o (PARI) a(n)=5*(n^2-n+2)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%o (Magma) [5*(n^2-n+2)/2 : n in [0..80]]; // _Wesley Ivan Hurt_, May 02 2021
%Y Essentially 5*A000124.
%Y Cf. A000217.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, Apr 25 2003
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