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A027980 a(n) = Sum_{k=0..n-1} T(n,k)*T(n,2n-k), T given by A027960. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A300337 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

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Last modified May 9 13:42 EDT 2021. Contains 343742 sequences. (Running on oeis4.)