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a(n) = 3 + 10*floor(n/2).
2

%I #23 Sep 08 2022 08:45:49

%S 3,13,13,23,23,33,33,43,43,53,53,63,63,73,73,83,83,93,93,103,103,113,

%T 113,123,123,133,133,143,143,153,153,163,163,173,173,183,183,193,193,

%U 203,203,213,213,223,223,233,233,243,243,253,253,263,263,273,273,283

%N a(n) = 3 + 10*floor(n/2).

%H Vincenzo Librandi, <a href="/A168437/b168437.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 a(n) = 10*n - a(n-1) - 4, with n>1, a(1) = 3.

%F a(n) = 10*floor(n/2) + 3 = A168641(n) + 3. - _Rick L. Shepherd_, Jun 17 2010

%F G.f.: x*(3 + 10*x - 3*x^2)/((1+x)*(x-1)^2). - _Vincenzo Librandi_, Sep 19 2013

%F a(n) = a(n-1) +a(n-2) -a(n-3). - _Vincenzo Librandi_, Sep 19 2013

%F a(n) = (1 + 5*(-1)^n + 10*n)/2. - _Bruno Berselli_, Sep 19 2013

%F E.g.f.: (1/2)*(5 - 6*exp(x) + (10*x + 1)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 22 2016

%t Table[3 + 10 Floor[n/2], {n, 70}] (* or *) CoefficientList[Series[(3 + 10 x - 3 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 19 2013 *)

%t LinearRecurrence[{1,1,-1},{3,13,13},70] (* _Harvey P. Dale_, May 26 2021 *)

%o (PARI) a(n)=n\2*10+3 \\ _Charles R Greathouse IV_, Jan 11 2012

%o (Magma) [3+10*Floor(n/2): n in [1..70]]; // _Vincenzo Librandi_, Sep 19 2013

%Y Bisections of A168437 are A017305 and (A017305 MINUS {3}). - _Rick L. Shepherd_, Jun 17 2010

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Nov 25 2009

%E Edited by _Rick L. Shepherd_, Jun 17 2010

%E Definition rewritten, using Shepherd's formula, by _Vincenzo Librandi_, Sep 19 2013