A027979 a(n) = Sum_{k=0..n} T(n,k)*T(n,2n-k), T given by A027960.

1, 10, 29, 97, 297, 904, 2685, 7876, 22823, 65533, 186691, 528370, 1486969, 4164382, 11613137, 32264089, 89339325, 246645436, 679111413, 1865340568, 5112351131, 13983383605, 38177371159, 104055773542, 283171508977

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-5,-5,5,-1).

Crossrefs

Cf. A000032, A000045, A027960.

Programs

GAP

List([0..40], n-> (n+1)*Lucas(1,-1,2*n)[2] + 3*Fibonacci(2*n) -(-1)^n ); # G. C. Greubel, Oct 01 2019

Magma

[(n+1)*Lucas(2*n) + 3*Fibonacci(2*n) -(-1)^n: n in [0..40]]; // G. C. Greubel, Oct 01 2019

Maple

f:= combinat[fibonacci]: seq((n+1)*(f(2*n+1) + f(2*n-1)) + 3*f(2*n) -(-1)^n, n=0..40); # G. C. Greubel, Oct 01 2019

Mathematica

Table[(n+1)*LucasL[2*n] +3*Fibonacci[2*n] -(-1)^n, {n,0,40}] (* G. C. Greubel, Oct 01 2019 *)

PARI

vector(41, n, f=fibonacci; n*(f(2*n-1) + f(2*n-3)) + 3*f(2*n-2) +(-1)^n) \\ G. C. Greubel, Oct 01 2019

Sage

[(n+1)*lucas_number2(2*n,1,-1) + 3*fibonacci(2*n) -(-1)^n for n in (0..40)] # G. C. Greubel, Oct 01 2019

Formula

G.f.: (1 +5*x -16*x^2 +7*x^3 +2*x^4)/((1+x)*(1-3*x+x^2)^2). - Colin Barker, Nov 25 2014

a(n) = (n+1)*Lucas(2*n) + 3*Fibonacci(2*n) - (-1)^n. - G. C. Greubel, Oct 01 2019