

A027980


a(n) = Sum_{k=0..n1} T(n,k)*T(n,2nk), 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
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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)*(13*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*n1))  f(2*n1) + (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



