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A041819 Denominators of continued fraction convergents to sqrt(430). 2
1, 1, 3, 4, 15, 19, 129, 1051, 6435, 7486, 28893, 36379, 101651, 138030, 5622851, 5760881, 17144613, 22905494, 85861095, 108766589, 738460629, 6016451621, 36837170355, 42853621976, 165398036283, 208251658259, 581901352801, 790153011060, 32188021795201, 32978174806261 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

G.f.: -(x^26 -x^25 +3*x^24 -4*x^23 +15*x^22 -19*x^21 +129*x^20 -1051*x^19 +6435*x^18 -7486*x^17 +28893*x^16 -36379*x^15 +101651*x^14 -138030*x^13 -101651*x^12 -36379*x^11 -28893*x^10 -7486*x^9 -6435*x^8 -1051*x^7 -129*x^6 -19*x^5 -15*x^4 -4*x^3 -3*x^2 -x -1)/(x^28 -5724502*x^14 +1). - Vincenzo Librandi, Dec 25 2013

a(n) = 5724502*a(n-14) - a(n-28) for n>27. - Vincenzo Librandi, Dec 25 2013

MATHEMATICA

Denominator[Convergents[Sqrt[430], 30]] (* or *) CoefficientList[Series[-(x^26 - x^25 + 3 x^24 - 4 x^23 + 15 x^22 - 19 x^21 + 129 x^20 - 1051 x^19 + 6435 x^18 - 7486 x^17 + 28893 x^16 - 36379 x^15 + 101651 x^14 - 138030 x^13 - 101651 x^12 - 36379 x^11 - 28893 x^10 - 7486 x^9 - 6435 x^8 - 1051 x^7 - 129 x^6 - 19 x^5 - 15 x^4 - 4 x^3 -3 x^2 - x - 1)/(x^28 - 5724502 x^14 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 25 2013 *)

CROSSREFS

Cf. A041818.

Sequence in context: A056742 A041435 A136210 * A095799 A109926 A272514

Adjacent sequences:  A041816 A041817 A041818 * A041820 A041821 A041822

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Dec 25 2013

STATUS

approved

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Last modified September 20 16:46 EDT 2019. Contains 327242 sequences. (Running on oeis4.)