cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A168459 a(n) = (10*n + 5*(-1)^n - 3)/2.

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%I A168459 #22 Sep 08 2022 08:45:49
%S A168459 1,11,11,21,21,31,31,41,41,51,51,61,61,71,71,81,81,91,91,101,101,111,
%T A168459 111,121,121,131,131,141,141,151,151,161,161,171,171,181,181,191,191,
%U A168459 201,201,211,211,221,221,231,231,241,241,251,251,261,261,271,271,281
%N A168459 a(n) = (10*n + 5*(-1)^n - 3)/2.
%H A168459 Vincenzo Librandi, <a href="/A168459/b168459.txt">Table of n, a(n) for n = 1..1000</a>
%H A168459 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A168459 a(n) = 10*n - a(n-1) - 8 with n>1, a(1)=1.
%F A168459 From _Bruno Berselli_, Sep 16 2013: (Start)
%F A168459 G.f.: x*(1 + 10*x - x^2)/((1+x)*(1-x)^2).
%F A168459 a(n) = A168457(n) - 1 = 2*A168282(n) - 1.
%F A168459 a(n) = a(n-1) +a(n-2) -a(n-3). (End)
%F A168459 a(n) = 1 + 10*floor(n/2). - _Vincenzo Librandi_, Sep 19 2013
%F A168459 E.g.f.: (1/2)*(5 - 2*exp(x) + (10*x - 3)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 23 2016
%t A168459 Table[5 n + 5 (-1)^n/2 - 3/2, {n, 60}] (* _Bruno Berselli_, Sep 16 2013 *)
%t A168459 Table[1 + 10 Floor[n/2], {n, 70}] (* or *) CoefficientList[Series[(1 + 10 x - x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 19 2013 *)
%o A168459 (Magma) [1+10*Floor(n/2): n in [1..70]]; // _Vincenzo Librandi_, Sep 19 2013
%Y A168459 Cf. A017281, A168457, A168282.
%K A168459 nonn,easy,less
%O A168459 1,2
%A A168459 _Vincenzo Librandi_, Nov 26 2009
%E A168459 New definition by _Bruno Berselli_, Sep 16 2013