login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A162273 a(n) = ((2+sqrt(3))*(3+sqrt(3))^n + (2-sqrt(3))*(3-sqrt(3))^n)/2. 1
2, 9, 42, 198, 936, 4428, 20952, 99144, 469152, 2220048, 10505376, 49711968, 235239552, 1113165504, 5267555712, 24926341248, 117952713216, 558158231808, 2641233111552, 12498449278464, 59143297001472, 279869086338048 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Binomial transform of A001075 without initial term 1, inverse binomial transform of A162274.

The INVERTi transform yields A007051 without A007051(0). - R. J. Mathar, Jul 07 2009

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n) = 6*a(n-1) - 6*a(n-2) for n > 1; a(0) = 2, a(1) = 9.

G.f.: (2-3*x)/(1-6*x+6*x^2).

MAPLE

seq(simplify(((2+sqrt(3))*(3+sqrt(3))^n+(2-sqrt(3))*(3-sqrt(3))^n)*1/2), n = 0 .. 22); # Emeric Deutsch, Jul 11 2009

PROG

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((2+r)*(3+r)^n+(2-r)*(3-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 05 2009

CROSSREFS

Cf. A001075, A162274.

Sequence in context: A192661 A020038 A056845 * A289684 A280955 A276508

Adjacent sequences:  A162270 A162271 A162272 * A162274 A162275 A162276

KEYWORD

nonn

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Jun 29 2009

EXTENSIONS

Edited and extended beyond a(5) by R. J. Mathar and Klaus Brockhaus, Jul 05 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 19 13:26 EDT 2019. Contains 324222 sequences. (Running on oeis4.)