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Convolution of natural numbers n >= 1 with Fibonacci numbers F(k), for k >= 6.
2

%I #8 Sep 08 2022 08:44:52

%S 8,29,71,147,278,498,862,1459,2433,4017,6588,10756,17508,28441,46139,

%T 74783,121138,196150,317530,513935,831733,1345949,2177976,3524232,

%U 5702528,9227093,14929967,24157419,39087758,63245562,102333718

%N Convolution of natural numbers n >= 1 with Fibonacci numbers F(k), for k >= 6.

%H G. C. Greubel, <a href="/A037157/b037157.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-1,1).

%F a(n) = Fibonacci(n+10) - (47+13*n).

%F G.f.: (8+5*x)/((1-x-x^2)*(1-x)^2).

%t Table[Fibonacci[n+10] -13*n-47, {n,0,40}] (* _G. C. Greubel_, Jul 05 2019 *)

%o (PARI) vector(40, n, n--; fibonacci(n+10) -13*n-47) \\ _G. C. Greubel_, Jul 05 2019

%o (Magma) [Fibonacci(n+10) -13*n-47: n in [0..40]]; // _G. C. Greubel_, Jul 05 2019

%o (Sage) [fibonacci(n+10) -13*n-47 for n in (0..40)] # _G. C. Greubel_, Jul 05 2019

%o (GAP) List([0..40], n-> Fibonacci(n+10) -13*n-47) # _G. C. Greubel_, Jul 05 2019

%Y Cf. A000045, A037140.

%K easy,nonn

%O 0,1

%A _Wolfdieter Lang_