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%I #26 Mar 15 2024 02:24:35
%S 5,5,14,14,23,23,32,32,41,41,50,50,59,59,68,68,77,77,86,86,95,95,104,
%T 104,113,113,122,122,131,131,140,140,149,149,158,158,167,167,176,176,
%U 185,185,194,194,203,203,212,212,221,221,230,230,239,239,248,248,257
%N a(n) = 9*n - a(n-1) - 8 with n>1, a(1)=5.
%H Vincenzo Librandi, <a href="/A168418/b168418.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 _R. J. Mathar_, Jan 26 2010: (Start)
%F a(n) = A168213(n-1), n>1.
%F G.f.: x*(5 + 4*x^2)/((1+x)*(x-1)^2). (End)
%F From _G. C. Greubel_, Jul 22 2016: (Start)
%F a(n) = a(n-1) + a(n-2) - a(n-3).
%F E.g.f.: (1/4)*(-9 + 16*exp(x) + (18*x - 7)*exp(2*x))*exp(-x). (End)
%t LinearRecurrence[{1, 1, -1}, {5, 5, 14}, 60] (* _Vincenzo Librandi_, Feb 27 2012 *)
%t RecurrenceTable[{a[1]==5,a[n]==9n-a[n-1]-8},a,{n,60}] (* or *) With[ {c= LinearRecurrence[{2,-1},{5,14},40]},Riffle[c,c]] (* or *) With[{c= 9* Range[ 40]-4}, Riffle[c,c]] (* _Harvey P. Dale_, Jan 25 2019 *)
%o (Magma) I:=[5, 5, 14]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..60]]; // _Vincenzo Librandi_, Feb 28 2012
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Nov 25 2009
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