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

0,1

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).

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).

Mathematica

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

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=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

Crossrefs

Cf. A162772, A162963.

Sequence in context: A037635 A154635 A062808 * A140637 A342963 A022026

Adjacent sequences: A162770 A162771 A162772 * A162774 A162775 A162776

Keyword

nonn

Author

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

Extensions

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

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

Status

approved