login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A027980 a(n) = Sum_{k=0..n-1} T(n,k)*T(n,2n-k), T given by A027960. 1

%I

%S 1,13,48,176,580,1844,5667,17047,50404,147090,424686,1215528,3453733,

%T 9752641,27393240,76587284,213260152,591707612,1636514439,4513276555,

%U 12414985996,34071252918,93305816418,255027755856,695815086025,1895348847349,5154987856512,14000952578552

%N a(n) = Sum_{k=0..n-1} T(n,k)*T(n,2n-k), T given by A027960.

%H G. C. Greubel, <a href="/A027980/b027980.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,-5,5,-1).

%F G.f.: (1 +8*x -12*x^2 +6*x^3)/ ((1+x)*(1-3*x+x^2)^2). - _Colin Barker_, Nov 25 2014

%F a(n) = (n+1)*Lucas(2*n) - Fibonacci(2*n+1) - (-1)^n. - _G. C. Greubel_, Oct 01 2019

%p with(combinat); f:=fibonacci; seq((n+1)*(f(2*n+3) + f(2*n+1)) - f(2*n+1) -(-1)^n, n=0..40); # _G. C. Greubel_, Oct 01 2019

%t Table[(n+1)*LucasL[2*n+2] -Fibonacci[2*n+1] -(-1)^n, {n,0,40}] (* _G. C. Greubel_, Oct 01 2019 *)

%o (PARI) vector(41, n, f=fibonacci; n*(f(2*n+1) + f(2*n-1)) - f(2*n-1) + (-1)^n) \\ _G. C. Greubel_, Oct 01 2019

%o (MAGMA) [(n+1)*Lucas(2*n+2) - Fibonacci(2*n+1) -(-1)^n: n in [0..40]]; // _G. C. Greubel_, Oct 01 2019

%o (Sage) [(n+1)*lucas_number2(2*n+2,1,-1) - fibonacci(2*n+1) -(-1)^n for n in (0..40)] # _G. C. Greubel_, Oct 01 2019

%o (GAP) List([0..40], n-> (n+1)*Lucas(1,-1,2*n+2)[2] - Fibonacci(2*n+1) -(-1)^n); # _G. C. Greubel_, Oct 01 2019

%Y Cf. A000032, A000045, A027960.

%K nonn

%O 0,2

%A _Clark Kimberling_

%E Terms a(24) onward added by _G. C. Greubel_, Oct 01 2019

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 21 00:35 EDT 2021. Contains 345328 sequences. (Running on oeis4.)