A030452 Markov numbers satisfying region 5 (x=5) of the equation x^2 + y^2 + z^2 = 3xyz.

1, 2, 13, 29, 194, 433, 2897, 6466, 43261, 96557, 646018, 1441889, 9647009, 21531778, 144059117, 321534781, 2151239746, 4801489937, 32124537073, 71700814274, 479716816349, 1070710724173, 7163627708162, 15988960048321

Offset

1,2

Comments

Positive values of x (or y) satisfying x^2 - 15xy + y^2 + 25 = 0. - Colin Barker, Feb 11 2014

Links

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

Eric Weisstein's World of Mathematics, Markov Number.

Index entries for linear recurrences with constant coefficients, signature (0,15,0,-1).

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

Adjacent sequences: A030449 A030450 A030451 * A030453 A030454 A030455

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