A093132 Third binomial transform of Fibonacci(3n+2).

1, 8, 60, 440, 3200, 23200, 168000, 1216000, 8800000, 63680000, 460800000, 3334400000, 24128000000, 174592000000, 1263360000000, 9141760000000, 66150400000000, 478668800000000, 3463680000000000, 25063424000000000

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 (10,-20).

Formula

G.f.: (1-2*x)/(1-10*x+20*x^2).

a(n) = ( (5 + 3*sqrt(5))*(5 + sqrt(5))^n + (5 - 3*sqrt(5))*(5 - sqrt(5))^n)/10.

a(n) = 2^n*A039717(n).

a(2*n) = 4^n*5^n*Fibonacci(2*n+2), a(2*n+1) = 2^(2*n+1)*5^n*Lucas(2*n+3). - G. C. Greubel, Dec 27 2019

Maple

seq(coeff(series((1-2*x)/(1-10*x+20*x^2), x, n+1), x, n), n = 0..30); # G. C. Greubel, Dec 27 2019

Mathematica

Table[If[EvenQ[n], 2^n*5^(n/2)*Fibonacci[n+2], 2^n*5^((n-1)/2)*LucasL[n+2]], {n, 0, 30}] (* G. C. Greubel, Dec 27 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec((1-2*x)/(1-10*x+20*x^2)) \\ G. C. Greubel, Dec 27 2019
(Magma) I:=[1, 8]; [n le 2 select I[n] else 10*(Self(n-1) - 2*Self(n-2)): n in [1..30]]; // G. C. Greubel, Dec 27 2019
(Sage)
def A093132_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1-2*x)/(1-10*x+20*x^2) ).list()
A093132_list(30) # G. C. Greubel, Dec 27 2019
(GAP) a:=[1, 8];; for n in [2..30] do a[n]:=10*(a[n-1]-2*a[n-2]); od; a; # G. C. Greubel, Dec 27 2019

Crossrefs

Cf. A000032, A000045, A039717.

Sequence in context: A002927 A274800 A126640 * A094169 A129325 A285391

Adjacent sequences: A093129 A093130 A093131 * A093133 A093134 A093135

Keyword

easy,nonn

Author

Paul Barry, Mar 23 2004

Status

approved