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A030452 Markov numbers satisfying region 5 (x=5) of the equation x^2 + y^2 + z^2 = 3xyz. 1
1, 2, 13, 29, 194, 433, 2897, 6466, 43261, 96557, 646018, 1441889, 9647009, 21531778, 144059117, 321534781, 2151239746, 4801489937, 32124537073, 71700814274, 479716816349, 1070710724173, 7163627708162, 15988960048321 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Positive values of x (or y) satisfying x^2 - 15xy + y^2 + 25 = 0. - Colin Barker, Feb 11 2014
LINKS
Eric Weisstein's World of Mathematics, Markov Number.
FORMULA
a(n) = 15*a(n-2)-a(n-4).
G.f.: -x*(x-1)*(x^2+3*x+1) / (x^4-15*x^2+1). - Colin Barker, Feb 11 2014
MATHEMATICA
CoefficientList[Series[(1 - x) (x^2 + 3 x + 1)/(x^4 - 15 x^2 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 12 2014 *)
PROG
(PARI) Vec(-x*(x-1)*(x^2+3*x+1)/(x^4-15*x^2+1) + O(x^100)) \\ Colin Barker, Feb 11 2014
(Magma) I:=[1, 2, 13, 29]; [n le 4 select I[n] else 15*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Feb 12 2014
CROSSREFS
Sequence in context: A299510 A299310 A300111 * A132602 A359125 A001914
KEYWORD
nonn,easy
AUTHOR
Mark Milhet (mm992395(AT)shellus.com)
EXTENSIONS
More terms from James A. Sellers, May 01 2000
Offset changed to 1 by Colin Barker, Feb 11 2014
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)