A042465 Denominators of continued fraction convergents to sqrt(760).

1, 1, 2, 7, 37, 44, 257, 815, 1072, 1887, 102970, 104857, 207827, 728338, 3849517, 4577855, 26738792, 84794231, 111533023, 196327254, 10713204739, 10909531993, 21622736732, 75777742189, 400511447677, 476289189866, 2781957397007, 8822161380887, 11604118777894

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, 104042, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^18 -x^17 +2*x^16 -7*x^15 +37*x^14 -44*x^13 +257*x^12 -815*x^11 +1072*x^10 -1887*x^9 -1072*x^8 -815*x^7 -257*x^6 -44*x^5 -37*x^4 -7*x^3 -2*x^2 -x -1) / (x^20 -104042*x^10 +1). - Colin Barker, Dec 14 2013

a(n) = 104042*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Jan 23 2014

Mathematica

Denominator[Convergents[Sqrt[760], 40]] (* Harvey P. Dale, Nov 03 2011 *)

Prog

(Magma) I:=[1, 1, 2, 7, 37, 44, 257, 815, 1072, 1887, 102970, 104857, 207827, 728338, 3849517, 4577855, 26738792, 84794231, 111533023, 196327254]; [n le 20 select I[n] else 104042*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Jan 24 2014

Crossrefs

Cf. A042464, A040732.

Sequence in context: A274904 A173827 A029990 * A041051 A175487 A216362

Adjacent sequences: A042462 A042463 A042464 * A042466 A042467 A042468

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 14 2013

Status

approved