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

0,2

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).

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

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 *)

Prog

(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
(Magma) [(n+1)*Lucas(2*n+2) - Fibonacci(2*n+1) -(-1)^n: n in [0..40]]; // 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
(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

Crossrefs

Cf. A000032, A000045, A027960.

Sequence in context: A355961 A135712 A225920 * A200254 A288746 A220707

Adjacent sequences: A027977 A027978 A027979 * A027981 A027982 A027983

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved