A042575 Denominators of continued fraction convergents to sqrt(816).

1, 1, 2, 7, 23, 76, 99, 175, 9899, 10074, 19973, 69993, 229952, 759849, 989801, 1749650, 98970201, 100719851, 199690052, 699790007, 2299060073, 7596970226, 9896030299, 17493000525, 989504059699, 1006997060224, 1996501119923, 6996500419993, 22986002379902

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,9998,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -x^13 +2*x^12 -7*x^11 +23*x^10 -76*x^9 +99*x^8 -175*x^7 -99*x^6 -76*x^5 -23*x^4 -7*x^3 -2*x^2 -x -1) / ((x^8 -100*x^4 +1)*(x^8 +100*x^4 +1)). - Colin Barker, Dec 18 2013

a(n) = 9998*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Jan 25 2014

Mathematica

Denominator/@Convergents[Sqrt[816], 30] (* Harvey P. Dale, Jun 14 2011 *)

Prog

(Magma) I:=[1, 1, 2, 7, 23, 76, 99, 175, 9899, 10074, 19973, 69993, 229952, 759849, 989801, 1749650]; [n le 16 select I[n] else 9998*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Jan 25 2014

Crossrefs

Cf. A042574, A040787.

Sequence in context: A030282 A291015 A273345 * A256030 A052924 A067324

Adjacent sequences: A042572 A042573 A042574 * A042576 A042577 A042578

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 18 2013

Status

approved