A042008 Numerators of continued fraction convergents to sqrt(527).

22, 23, 505, 528, 23737, 24265, 533302, 557567, 25066250, 25623817, 563166407, 588790224, 26469936263, 27058726487, 594703192490, 621761918977, 27952227627478, 28573989546455, 628006008103033

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, 1056, 0, 0, 0, -1).

Formula

G.f.: -(x^7-22*x^6+23*x^5-505*x^4-528*x^3-505*x^2-23*x-22)/(x^8-1056*x^4+1). - Vincenzo Librandi, Nov 13 2013

a(n) = 1056*a(n-4)-a(n-8). - Vincenzo Librandi, Nov 13 2013

Mathematica

Numerator[Convergents[Sqrt[527], 30]] (* or *) CoefficientList[Series[-(x^7 - 22 x^6 + 23 x^5 - 505 x^4 - 528 x^3 - 505 x^2 - 23 x - 22)/(x^8 - 1056 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 13 2013 *)
LinearRecurrence[{0, 0, 0, 1056, 0, 0, 0, -1}, {22, 23, 505, 528, 23737, 24265, 533302, 557567}, 30] (* Harvey P. Dale, Sep 01 2017 *)

Prog

(Magma) I:=[22, 23, 505, 528, 23737, 24265, 533302, 557567]; [n le 8 select I[n] else 1056*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 13 2013

Crossrefs

Cf. A042009.

Sequence in context: A119603 A042004 A042006 * A042009 A042010 A162334

Adjacent sequences: A042005 A042006 A042007 * A042009 A042010 A042011

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved