A041819 Denominators of continued fraction convergents to sqrt(430).

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

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5724502, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

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: A338123 A041435 A136210 * A369910 A095799 A109926

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