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A042008 Numerators of continued fraction convergents to sqrt(527). 2
22, 23, 505, 528, 23737, 24265, 533302, 557567, 25066250, 25623817, 563166407, 588790224, 26469936263, 27058726487, 594703192490, 621761918977, 27952227627478, 28573989546455, 628006008103033 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
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
KEYWORD
nonn,cofr,frac,easy,less
AUTHOR
STATUS
approved

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Last modified June 14 13:28 EDT 2024. Contains 373400 sequences. (Running on oeis4.)