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%I #35 Feb 23 2023 03:49:30
%S 5,0,7,2,9,4,11,6,13,8,15,10,17,12,19,14,21,16,23,18,25,20,27,22,29,
%T 24,31,26,33,28,35,30,37,32,39,34,41,36,43,38,45,40,47,42,49,44,51,46,
%U 53,48,55,50,57,52,59,54,61,56,63,58,65,60,67,62,69,64,71,66,73
%N a(n) = 2*n - a(n-1) + 1 with n>1, a(1)=5.
%H Vincenzo Librandi, <a href="/A168195/b168195.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_, Nov 22 2009: (Start)
%F a(n) = a(n-1) + a(n-2) - a(n-3) = n + 1 - 3*(-1)^n.
%F G.f.: x*(5+2*x^2-5*x)/((1+x)*(x-1)^2). (End)
%F a(n) = n - 4 + 2^(2-(-1)^n). - _Wesley Ivan Hurt_, Dec 13 2013
%F a(n) = A004442(n-1) + 2*(1-(-1)^n) = A147677(n) - floor((n+3)/2). - _Filip Zaludek_, Oct 31 2016
%F Sum_{n>=3} (-1)^n/a(n) = 23/15 - log(2). - _Amiram Eldar_, Feb 23 2023
%p A168195:=n->n+1-3*(-1)^n; seq(A168195(n), n=1..100); # _Wesley Ivan Hurt_, Dec 13 2013
%t LinearRecurrence[{1,1,-1},{5,0,7},30] (* _Vincenzo Librandi_, Feb 27 2012 *)
%o (Magma) I:=[5,0,7]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Feb 27 2012
%Y Cf. A004442, A147677.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Nov 20 2009
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