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Fibonacci sequence beginning 29, 31.
2

%I #24 Sep 08 2022 08:45:42

%S 29,31,60,91,151,242,393,635,1028,1663,2691,4354,7045,11399,18444,

%T 29843,48287,78130,126417,204547,330964,535511,866475,1401986,2268461,

%U 3670447,5938908,9609355,15548263,25157618,40705881,65863499,106569380

%N Fibonacci sequence beginning 29, 31.

%H Harvey P. Dale, <a href="/A157681/b157681.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1).

%F a(n) = a(n-1) + a(n-2), a(0)=29, a(1)=31.

%F From _G. C. Greubel_, Nov 17 2018: (Start)

%F a(n) = 27*Fibonacci(n) + 2*Fibonacci(n+1).

%F G.f.: x*(29+2*x)/(1-x-x^2). (End)

%t LinearRecurrence[{1,1},{29,31},40] (* _Harvey P. Dale_, Dec 05 2014 *)

%t Table[27*Fibonacci[n] +2*Fibonacci[n+1], {n, 1, 40}] (* _G. C. Greubel_, Nov 17 2018 *)

%o (PARI) vector(40, n, 27*fibonacci(n) + 2*fibonacci(n+1)) \\ _G. C. Greubel_, Nov 17 2018

%o (Magma) [27*Fibonacci(n) + 2*Fibonacci(n+1): n in [1..40]]; // _G. C. Greubel_, Nov 17 2018

%o (Sage) [27*fibonacci(n)+2*fibonacci(n+1) for n in (1..10)] # _G. C. Greubel_, Nov 17 2018

%o (GAP) List([1..40], n -> 27*Fibonacci(n)+2*Fibonacci(n+1)); # _G. C. Greubel_, Nov 17 2018

%K nonn,easy

%O 1,1

%A _Kyle D. Balliet_, Mar 04 2009