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A027979 a(n) = Sum_{k=0..n} T(n,k)*T(n,2n-k), T given by A027960. 1
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 (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 +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

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 *)

PROG

(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

(MAGMA) [(n+1)*Lucas(2*n) + 3*Fibonacci(2*n) -(-1)^n: n in [0..40]]; // 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

(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

CROSSREFS

Cf. A000032, A000045, A027960.

Sequence in context: A200185 A321140 A301571 * A181102 A057456 A002422

Adjacent sequences:  A027976 A027977 A027978 * A027980 A027981 A027982

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified June 20 08:43 EDT 2021. Contains 345162 sequences. (Running on oeis4.)