A163065 a(n) = ((3+sqrt(5))*(5+sqrt(5))^n + (3-sqrt(5))*(5-sqrt(5))^n)/2.

3, 20, 140, 1000, 7200, 52000, 376000, 2720000, 19680000, 142400000, 1030400000, 7456000000, 53952000000, 390400000000, 2824960000000, 20441600000000, 147916800000000, 1070336000000000, 7745024000000000, 56043520000000000

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Jul 20 2009

Keywords

• nonn

Comments

Binomial transform of A163064. Fifth binomial transform of A163114.

10^(floor(n/2)) | a(n). - G. C. Greubel, Dec 22 2017

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-20).

Crossrefs

Cf. A163064, A163114.

Programs

Magma

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-5); S:=[ ((3+r)*(5+r)^n+(3-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 21 2009

Magma

I:=[3,20]; [n le 2 select I[n] else 10*Self(n-1) - 20*Self(n-2): n in [1..30]]; // G. C. Greubel, Dec 22 2017

Mathematica

CoefficientList[Series[(3-10*x)/(1-10*x+20*x^2), {x,0,50}], x] (* or *) LinearRecurrence[{10,-20}, {3,20}, 30] (* G. C. Greubel, Dec 22 2017 *)

PARI

x='x+O('x^30); Vec((3-10*x)/(1-10*x+20*x^2)) \\ G. C. Greubel, Dec 22 2017

Formula

a(n) = 10*a(n-1) - 20*a(n-2) for n > 1; a(0) = 3, a(1) = 20.

G.f.: (3-10*x)/(1-10*x+20*x^2).

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 21 2009