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%I #35 Mar 19 2024 09:34:03
%S 5,5,13,13,21,21,29,29,37,37,45,45,53,53,61,61,69,69,77,77,85,85,93,
%T 93,101,101,109,109,117,117,125,125,133,133,141,141,149,149,157,157,
%U 165,165,173,173,181,181,189,189,197,197,205,205,213,213,221,221,229,229
%N a(n) = 5 + 8*floor((n-1)/2).
%H Vincenzo Librandi, <a href="/A168392/b168392.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) = 8*n - a(n-1) - 6 with n>1, a(1)=5.
%F a(1) = 5, a(2)=5, a(3)=13; for n>3, a(n) = a(n-1) +a(n-2) -a(n-3). - _Harvey P. Dale_, Jan 27 2013
%F G.f.: x*(5 + 3*x^2)/((1+x)*(x-1)^2). - _Vincenzo Librandi_, Sep 18 2013
%F E.g.f.: (-2 + 3*exp(x) + (4*x - 1)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 19 2016
%F a(n) = A168379(n) - 2. - _Filip Zaludek_, Nov 01 2016
%t RecurrenceTable[{a[1]==5,a[n]==8n-a[n-1]-6},a,{n,80}] (* or *) LinearRecurrence[{1,1,-1},{5,5,13},80] (* or *) With[{c= LinearRecurrence[ {2,-1},{5,13},40]}, Riffle[c,c]] (* _Harvey P. Dale_, Jan 27 2013 *)
%t Table[5 + 8 Floor[(n - 1)/2], {n, 60}] (* _Bruno Berselli_, Sep 18 2013 *)
%t CoefficientList[Series[(5 + 3 x^2)/((1 + x) (x - 1)^2),{x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 18 2013 *)
%o (Magma) [5+8*Floor((n-1)/2): n in [1..70]]; // _Vincenzo Librandi_, Sep 18 2013
%Y Cf. A004770, A168379.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Nov 24 2009
%E New definition by _Vincenzo Librandi_, Sep 18 2013
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