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a(n) = (F(n+1)+L(n)+n)^2 where F(n) are the Fibonacci numbers (A000045) and L(n) are the Lucas numbers (A000032).
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%I #13 Oct 04 2017 15:34:50

%S 9,9,49,100,256,576,1369,3249,7921,19600,49284,125316,321489,829921,

%T 2152089,5597956,14592400,38093584,99540529,260273689,680844649,

%U 1781515264,4662431524,12203620900,31944770361,83624494041,218918244769,573112589764,1500389809216

%N a(n) = (F(n+1)+L(n)+n)^2 where F(n) are the Fibonacci numbers (A000045) and L(n) are the Lucas numbers (A000032).

%H Colin Barker, <a href="/A014718/b014718.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (7,-16,7,23,-28,-3,17,-4,-3,1).

%F G.f.: -(4*x^9-8*x^8+36*x^7-115*x^6+86*x^5+70*x^4-162*x^3+130*x^2-54*x+9) / ((x-1)^3*(x+1)*(x^2-3*x+1)*(x^2+x-1)^2). - _Colin Barker_, Apr 24 2015

%t Table[(Fibonacci[n+1]+LucasL[n]+n)^2,{n,0,50}] (* or *) LinearRecurrence[ {7,-16,7,23,-28,-3,17,-4,-3,1},{9,9,49,100,256,576,1369,3249,7921,19600},50] (* _Harvey P. Dale_, Oct 04 2017 *)

%o (PARI) lucas(n) = if(n==0, 2, fibonacci(2*n)/fibonacci(n))

%o a(n) = (fibonacci(n+1)+lucas(n)+n)^2 \\ _Colin Barker_, Apr 24 2015

%o (PARI) Vec(-(4*x^9-8*x^8+36*x^7-115*x^6+86*x^5+70*x^4-162*x^3+130*x^2-54*x+9) / ((x-1)^3*(x+1)*(x^2-3*x+1)*(x^2+x-1)^2) + O(x^100)) \\ _Colin Barker_, Apr 24 2015

%o (PARI) a(n)=(fibonacci(n-1)+2*fibonacci(n+1)+n)^2 \\ _Charles R Greathouse IV_, Apr 24 2015

%Y Cf. A000032, A000045.

%K nonn,easy

%O 0,1

%A _Mohammad K. Azarian_

%E Name corrected by _Colin Barker_, Apr 24 2015