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A042650 Numerators of continued fraction convergents to sqrt(855). 2
29, 117, 731, 3041, 177109, 711477, 4445971, 18495361, 1077176909, 4327202997, 27040394891, 112488782561, 6551389783429, 26318047916277, 164459677281091, 684156757040641, 39845551585638269, 160066363099593717 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
G.f.: (29 +117*x +731*x^2 +3041*x^3 +731*x^4 -117*x^5 +29*x^6 -x^7)/(1 -6082*x^4 +x^8). - Vincenzo Librandi, Nov 30 2013
a(n) = 6082*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 30 2013
MATHEMATICA
Numerator[Convergents[Sqrt[855], 30]] (* or *) CoefficientList[Series[(29 + 117 x + 731 x^2 + 3041 x^3 + 731 x^4 - 117 x^5 + 29 x^6 - x^7)/(1 - 6082 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 30 2013 *)
LinearRecurrence[{0, 0, 0, 6082, 0, 0, 0, -1}, {29, 117, 731, 3041, 177109, 711477, 4445971, 18495361}, 20] (* Harvey P. Dale, Oct 22 2017 *)
PROG
(Magma) I:=[29, 117, 731, 3041, 177109, 711477, 4445971, 18495361]; [n le 8 select I[n] else 6082*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 30 2013
CROSSREFS
Cf. A042651.
Sequence in context: A188359 A042648 A233046 * A158560 A330811 A118614
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved

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Last modified February 25 17:36 EST 2024. Contains 370332 sequences. (Running on oeis4.)