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A041805 Denominators of continued fraction convergents to sqrt(423). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 15 03:16 EDT 2019. Contains 328025 sequences. (Running on oeis4.)