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%I #22 Sep 08 2022 08:44:58
%S 6,281,13201,620166,29134601,1368706081,64300051206,3020733700601,
%T 141910183877041,6666757908520326,313195711516578281,
%U 14713531683370658881,691222793406904389126,32472757758441135630041,1525528391853326470222801,71667361659347902964841606
%N a(n) = (F(8*n+7)+F(8*n+5))/3, where F=A000045 (the Fibonacci sequence).
%H Colin Barker, <a href="/A049679/b049679.txt">Table of n, a(n) for n = 0..500</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (47,-1).
%F From _Philippe Deléham_, Nov 18 2008: (Start)
%F a(n) = 47*a(n-1) - a(n-2), a(0)=6, a(1)=281.
%F G.f.: (6-x)/(1-47*x+x^2). (End)
%F a(n) = (((5+3*sqrt(5))*(2/(47+21*sqrt(5)))^n + (1/2*(47+21*sqrt(5)))^n*(1885+843*sqrt(5))))/(315+141*sqrt(5)). - _Colin Barker_, May 05 2016
%t LinearRecurrence[{47,-1},{6,281},20] (* _Harvey P. Dale_, Dec 14 2014 *)
%t Table[(Fibonacci[8*n+7]+Fibonacci[8*n+5])/3, {n,0,30}] (* _G. C. Greubel_, Dec 02 2017 *)
%o (PARI) Vec((6-x)/(1-47*x+x^2) + O(x^20)) \\ _Colin Barker_, May 05 2016
%o (Magma) [(Fibonacci(8*n+7) + Fibonacci(8*n+5))/3: n in [0..30]]; // _G. C. Greubel_, Dec 02 2017
%o (PARI) for(n=0,30, print1((fibonacci(8*n+7) + fibonacci(8*n+5))/3, ", ")) \\ _G. C. Greubel_, Dec 02 2017
%K nonn,easy
%O 0,1
%A _Clark Kimberling_
%E Corrected and extended by _T. D. Noe_, Nov 07 2006
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