A163072 a(n) = ((4+sqrt(5))*(5+sqrt(5))^n + (4-sqrt(5))*(5-sqrt(5))^n)/2.

4, 25, 170, 1200, 8600, 62000, 448000, 3240000, 23440000, 169600000, 1227200000, 8880000000, 64256000000, 464960000000, 3364480000000, 24345600000000, 176166400000000, 1274752000000000, 9224192000000000, 66746880000000000

Offset: 0

Author

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

Keywords

• nonn

Comments

Binomial transform of A108404 without initial 1. Fifth binomial transform of A163141.

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. A108404, A163141.

Programs

Magma

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-5); S:=[ ((4+r)*(5+r)^n+(4-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 21 2009

Mathematica

LinearRecurrence[{10, -20}, {4, 25}, 30] (* G. C. Greubel, Jan 08 2018 *)

PARI

x='x+O('x^30); Vec((4-15*x)/(1-10*x+20*x^2)) \\ G. C. Greubel, Jan 08 2018

Formula

a(n) = 10*a(n-1) - 20*a(n-2) for n > 1; a(0) = 4, a(1) = 25.

G.f.: (4-15*x)/(1-10*x+20*x^2).

Extensions

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