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a(n) = (11 + 18*n + 9*(-1)^n)/4.
2

%I #26 Sep 08 2022 08:45:48

%S 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 185,185,194,194,203,203,212,212,221,221,230,230,239,239,248,248,257,257

%N a(n) = (11 + 18*n + 9*(-1)^n)/4.

%C Essentially the same as A168418.

%H Vincenzo Librandi, <a href="/A168213/b168213.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 05 2011: (Start)

%F a(n) = 9*n - a(n-1) + 1 for n > 1.

%F G.f.: x*(5 + 9*x - 5*x^2)/( (1+x)*(x-1)^2 ). (End)

%F E.g.f.: (1/4)*(9 - 20*exp(x) + (11 + 18*x)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 16 2016

%F a(n) = a(n-1) + a(n-2) - a(n-3). - _Wesley Ivan Hurt_, Aug 17 2021

%p A168213:=n->(11 + 18*n + 9*(-1)^n)/4: seq(A168213(n), n=1..100); # _Wesley Ivan Hurt_, Apr 26 2017

%t LinearRecurrence[{1, 1, -1}, {5, 14, 14}, 60] (* _Vincenzo Librandi_, Feb 28 2012 *)

%o (Magma) I:=[5, 14, 14]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Feb 28 2012

%o (PARI) a(n)=(11+18*n+9*(-1)^n)/4 \\ _Charles R Greathouse IV_, Jul 16 2016

%Y Cf. A168418.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Nov 20 2009