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A166863 a(1)= 1; a(2)= 5; thereafter a(n)= a(n-1) + a(n-2) + 5. 5

%I

%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 *)

%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,changed

%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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Last modified April 7 01:10 EDT 2020. Contains 333291 sequences. (Running on oeis4.)