A162773 a(n) = ((2+sqrt(5))*(5+sqrt(5))^n + (2-sqrt(5))*(5-sqrt(5))^n)/2.

2, 15, 110, 800, 5800, 42000, 304000, 2200000, 15920000, 115200000, 833600000, 6032000000, 43648000000, 315840000000, 2285440000000, 16537600000000, 119667200000000, 865920000000000, 6265856000000000, 45340160000000000

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Jul 13 2009

Keywords

• nonn

Comments

Binomial transform of A162772. Fifth binomial transform of A162963.

Links

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

Crossrefs

Cf. A162772, A162963.

Programs

Magma

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

Mathematica

LinearRecurrence[{10,-20},{2,15},30] (* Harvey P. Dale, Dec 24 2012 *)

Formula

a(n) = 10*a(n-1) - 20*a(n-2) for n > 1; a(0) = 2, a(1) = 15.

G.f.: (2-5*x)/(1-10*x+20*x^2).

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 19 2009

Formulae corrected and clarified by Harvey P. Dale, Dec 24 2012