A041805 Denominators of continued fraction convergents to sqrt(423).

1, 1, 2, 7, 30, 97, 127, 224, 9087, 9311, 18398, 64505, 276418, 893759, 1170177, 2063936, 83727617, 85791553, 169519170, 594349063, 2546915422, 8235095329, 10782010751, 19017106080, 771466253951, 790483360031, 1561949613982, 5476332201977, 23467278421890

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, 9214, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^14 -x^13 +2*x^12 -7*x^11 +30*x^10 -97*x^9 +127*x^8 -224*x^7 -127*x^6 -97*x^5 -30*x^4 -7*x^3 -2*x^2 -x -1) / ((x^8 -96*x^4 +1)*(x^8 +96*x^4 +1)). - Colin Barker, Nov 25 2013

a(n) = 9214*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 24 2013

Mathematica

Denominator[Convergents[Sqrt[423], 30]] (* Vincenzo Librandi, Dec 24 2013 *)

Prog

(Magma) I:=[1, 1, 2, 7, 30, 97, 127, 224, 9087, 9311, 18398, 64505, 276418, 893759, 1170177, 2063936]; [n le 16 select I[n] else 9214*Self(n-8)-Self(n-16): n in [1..50]]; // Vincenzo Librandi, Dec 24 2013

Crossrefs

Cf. A041804, A040402.

Sequence in context: A270526 A037417 A042913 * A173233 A074416 A325577

Adjacent sequences: A041802 A041803 A041804 * A041806 A041807 A041808

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 25 2013

Status

approved