A042278 Numerators of continued fraction convergents to sqrt(665).

25, 26, 103, 129, 361, 851, 2063, 2914, 10805, 13719, 696755, 710474, 2828177, 3538651, 9905479, 23349609, 56604697, 79954306, 296467615, 376421921, 19117563665, 19493985586, 77599520423, 97093506009, 271786532441, 640666570891, 1553119674223, 2193786245114

Offset

0,1

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, 27438, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^19 -25*x^18 +26*x^17 -103*x^16 +129*x^15 -361*x^14 +851*x^13 -2063*x^12 +2914*x^11 -10805*x^10 -13719*x^9 -10805*x^8 -2914*x^7 -2063*x^6 -851*x^5 -361*x^4 -129*x^3 -103*x^2 -26*x -25) / (x^20 -27438*x^10 +1). - Colin Barker, Dec 06 2013

Maple

convert(sqrt(665), confrac, 30, cvgts): numer(cvgts); # Wesley Ivan Hurt, Dec 07 2013

Mathematica

Numerator[Convergents[Sqrt[665], 30]] (* Vincenzo Librandi, Nov 20 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 27438, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {25, 26, 103, 129, 361, 851, 2063, 2914, 10805, 13719, 696755, 710474, 2828177, 3538651, 9905479, 23349609, 56604697, 79954306, 296467615, 376421921}, 30] (* Harvey P. Dale, Jul 04 2021 *)

Crossrefs

Cf. A042279, A040639.

Sequence in context: A042270 A042268 A042266 * A042276 A042282 A042280

Adjacent sequences: A042275 A042276 A042277 * A042279 A042280 A042281

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 06 2013

Status

approved