A027980 a(n) = Sum_{k=0..n-1} T(n,k)*T(n,2n-k), T given by A027960.

1, 13, 48, 176, 580, 1844, 5667, 17047, 50404, 147090, 424686, 1215528, 3453733, 9752641, 27393240, 76587284, 213260152, 591707612, 1636514439, 4513276555, 12414985996, 34071252918, 93305816418, 255027755856, 695815086025, 1895348847349, 5154987856512, 14000952578552

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)[2] - Fibonacci(2*n+1) -(-1)^n); # G. C. Greubel, Oct 01 2019

Magma

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

Maple

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

Mathematica

Table[(n+1)*LucasL[2*n+2] -Fibonacci[2*n+1] -(-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-1)) - f(2*n-1) + (-1)^n) \\ G. C. Greubel, Oct 01 2019

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

Formula

G.f.: (1 +8*x -12*x^2 +6*x^3)/ ((1+x)*(1-3*x+x^2)^2). - Colin Barker, Nov 25 2014

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

Extensions

Terms a(24) onward added by G. C. Greubel, Oct 01 2019