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 A173299 Numerators of fractions x^n + y^n, where x + y = 1 and x^2 + y^2 = 2. 4
 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. - 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: # R. J. Mathar, Mar 01 2010 MATHEMATICA Module[{x=(1-Sqrt[3])/2, y}, y=1-x; Table[x^n+y^n, {n, 40}]]//Simplify// Numerator (* Harvey P. Dale, Aug 24 2019 *) PROG (PARI) { a(n) = numerator( 2 * polcoeff( lift( Mod((1+x)/2, x^2-3)^n ), 0) ) } (MAGMA) Z:=PolynomialRing(Integers()); N:=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] ]; // Klaus Brockhaus, Mar 02 2010 CROSSREFS Cf. A173300 (denominators). Sequence in context: A306918 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

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Last modified January 28 01:36 EST 2021. Contains 340489 sequences. (Running on oeis4.)