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%I #25 Jan 29 2021 13:30:21
%S 1,5,11,21,37,63,105,173,283,461,749,1215,1969,3189,5163,8357,13525,
%T 21887,35417,57309,92731,150045,242781,392831,635617,1028453,1664075,
%U 2692533,4356613,7049151,11405769,18454925,29860699,48315629,78176333,126491967
%N a(1)= 1; a(2)= 5; thereafter a(n)= a(n-1) + a(n-2) + 5.
%H Reinhard Zumkeller, <a href="/A166863/b166863.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 (2,0,-1).
%F a(n) = A154691(n) - 2 = 2*A000045(n+3) - 5. - _R. J. Mathar_, Oct 26 2009
%F From _R. J. Mathar_, Oct 26 2009: (Start)
%F a(n) = 2*a(n-1) - a(n-3).
%F G.f: x*(1+3*x+x^2)/((x-1)* (x^2+x-1)). (End)
%F a(n+1) = a(n) + 2*A000045(n+2). - _Reinhard Zumkeller_, Nov 17 2013
%e a(3) = 5 + 1 + 5 = 11.
%t 2 * Fibonacci[Range[4,4! ]] - 5 (* _Vladimir Joseph Stephan Orlovsky_, Mar 19 2010 *)
%t RecurrenceTable[{a[1]==1,a[2]==5,a[n]==a[n-1]+a[n-2]+5},a,{n,40}] (* or *) LinearRecurrence[{2,0,-1},{1,5,11},40] (* _Harvey P. Dale_, Jan 29 2021 *)
%o (Haskell)
%o a166863 n = a166863_list !! (n-1)
%o a166863_list = 1 : zipWith (+) a166863_list (drop 3 $ map (* 2) a000045_list)
%o -- _Reinhard Zumkeller_, Nov 17 2013
%Y Cf. A001595, A154691.
%K easy,nonn
%O 1,2
%A _Geoff Ahiakwo_, Oct 22 2009
%E Missing value for a(29) inserted by _Reinhard Zumkeller_, Nov 17 2013
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