

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

Vincenzo Librandi, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Markov Number.
Index to sequences with linear recurrences with constant coefficients, signature (0,15,0,1).


FORMULA

a(n) = 15*a(n2)a(n4).
G.f.: x*(x1)*(x^2+3*x+1) / (x^415*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*(x1)*(x^2+3*x+1)/(x^415*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(n2)Self(n4): n in [1..30]]; // Vincenzo Librandi, Feb 12 2014


CROSSREFS

Sequence in context: A042917 A174049 A141336 * A132602 A001914 A031392
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



