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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A173299 Numerators of fractions x^n + y^n, where x + y = 1 and x^2 + y^2 = 2. 3
1, 2, 5, 7, 19, 13, 71, 97, 265, 181, 989, 1351, 3691, 2521, 13775, 18817, 51409, 35113, 191861, 262087, 716035, 489061, 2672279, 3650401, 9973081, 6811741, 37220045, 50843527, 138907099, 94875313, 518408351, 708158977, 1934726305, 1321442641 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

x and y are given by -A152422 and 1-A152422. [From R. J. Mathar, Mar 01 2010]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

FORMULA

a(n) = numerator of ((1+sqrt(3))/2)^n + ((1-sqrt(3))/2)^n

EXAMPLE

a(3) = 5 because x^3 + y^3 is 2.5 and 2.5 is 5/2.

MAPLE

A173299 := proc(n) local x, y ; x := (1+sqrt(3))/2 ; y := (1-sqrt(3))/2 ; expand(x^n+y^n) ; numer(%) ; end proc: [From R. J. Mathar, Mar 01 2010]

PROG

(PARI) { a(n) = numerator( 2 * polcoeff( lift( Mod((1+x)/2, x^2-3)^n ), 0) ) }

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(2*x^2-2*x-1); S:=[ r^n+(1-r)^n: n in [1..34] ]; [ Numerator(RationalField()!S[j]): j in [1..#S] ]; [From Klaus Brockhaus, Mar 02 2010]

CROSSREFS

Cf. A173300 (denominators)

Sequence in context: A099357 A027038 A173929 * A097052 A102937 A045358

Adjacent sequences:  A173296 A173297 A173298 * A173300 A173301 A173302

KEYWORD

nonn,frac

AUTHOR

J. Lowell, Feb 15 2010

EXTENSIONS

Formula, more terms, and PARI script from Max Alekseyev, Feb 24 2010

More terms from Klaus Brockhaus and R. J. Mathar, Mar 01 2010

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 30 04:42 EDT 2017. Contains 284296 sequences.