A042168 Numerators of continued fraction convergents to sqrt(609).

24, 25, 74, 691, 765, 1456, 9501, 10957, 20458, 195079, 410616, 605695, 29483976, 30089671, 89663318, 837059533, 926722851, 1763782384, 11509417155, 13273199539, 24782616694, 236316749785, 497416116264, 733732866049, 35716593686616, 36450326552665

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, 0, 0, 1211390, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^23 -24*x^22 +25*x^21 -74*x^20 +691*x^19 -765*x^18 +1456*x^17 -9501*x^16 +10957*x^15 -20458*x^14 +195079*x^13 -410616*x^12 -605695*x^11 -410616*x^10 -195079*x^9 -20458*x^8 -10957*x^7 -9501*x^6 -1456*x^5 -765*x^4 -691*x^3 -74*x^2 -25*x -24) / (x^24 -1211390*x^12 +1). - Colin Barker, Dec 03 2013

a(n) = 1211390*a(n-12) - a(n-24). - Wesley Ivan Hurt, Jan 20 2024

Mathematica

Numerator/@Convergents[Sqrt[609], 30] (* Harvey P. Dale, Jun 07 2011 *)

Crossrefs

Cf. A042169, A040584.

Sequence in context: A042172 A042174 A042170 * A042178 A042180 A042176

Adjacent sequences: A042165 A042166 A042167 * A042169 A042170 A042171

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 03 2013

Status

approved