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%I #19 Jul 20 2023 11:06:22
%S 0,610,1596,16500,97410,707560,4744080,32791746,224035980,1537454500,
%T 10532923170,72206679000,494878036896,3392033285410,23249109634140,
%U 159352376426580,1092215843858370,7486162932788296,51310913160533040
%N Expansion of 2*x^2*(305-727*x-315*x^2+60*x^3)/((1-x)*(1-7*x+x^2)*(1+3*x+x^2)).
%H G. C. Greubel, <a href="/A120719/b120719.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,15,-15,-5,1).
%F G.f.: 2*x^2*(305-727*x-315*x^2+60*x^3)/((1-x)*(1-7*x+x^2)*(1+3*x+x^2)). - _Colin Barker_, Nov 01 2012
%F a(n) = -120*[n=0] + (2/25)*(677 + (2/3)*(37*Fibonacci(4*n+4) + 28*Fibonacci(4*n)) + (-1)^n*(749*Fibonacci(2*n+2) - 996*Fibonacci(2*n))). - _G. C. Greubel_, Jul 20 2023
%t LinearRecurrence[{5,15,-15,-5,1}, {0,610,1596,16500,97410}, 40] (* _G. C. Greubel_, Jul 20 2023 *)
%o (Magma)
%o F:=Fibonacci;
%o A120719:= func< n | (2/25)*(677 +(2/3)*(37*F(4*n+4) +28*F(4*n)) +(-1)^n*(749*F(2*n+2) -996*F(2*n))) >;
%o [A120719(n): n in [1..40]]; // _G. C. Greubel_, Jul 20 2023
%o (SageMath)
%o F=fibonacci
%o def A120719(n): return (2/25)*(677 +(2/3)*(37*F(4*n+4) +28*F(4*n)) +(-1)^n*(749*F(2*n+2) -996*F(2*n)))
%o [A120719(n) for n in range(1,41)] # _G. C. Greubel_, Jul 20 2023
%Y Cf. A001906, A004187.
%K nonn,easy
%O 1,2
%A _Roger L. Bagula_, Aug 13 2006
%E Meaningful name from _Joerg Arndt_, Dec 26 2022
%E Edited by _G. C. Greubel_, Jul 20 2023
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