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A042778
Numerators of continued fraction convergents to sqrt(920).
2
30, 91, 5490, 16561, 999150, 3014011, 181839810, 548533441, 33093846270, 99830072251, 6022898181330, 18168524616241, 1096134375155790, 3306571650083611, 199490433380172450, 601777871790600961, 36306162740816230110, 109520266094239291291, 6607522128395173707570
OFFSET
0,1
FORMULA
G.f.: (30 + 91*x + 30*x^2 - x^3)/(1 - 182*x^2 + x^4). - Vincenzo Librandi, Dec 04 2013, simplified by Colin Barker, Dec 23 2013
a(n) = 33122*a(n-4) - a(n-8) = 182*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 04 2013, reduced by Bruno Berselli, Dec 23 2013
MATHEMATICA
Numerator[Convergents[Sqrt[920], 30]] (* or *) CoefficientList[Series[(30 + 91 x + 30 x^2 - x^3)/(1 - 182 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 04 2013 *)
LinearRecurrence[{0, 182, 0, -1}, {30, 91, 5490, 16561}, 30] (* Harvey P. Dale, Oct 20 2024 *)
PROG
(Magma) I:=[30, 91, 5490, 16561]; [n le 4 select I[n] else 182*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 04 2013, reduced by Bruno Berselli, Dec 23 2013
CROSSREFS
Sequence in context: A306121 A042774 A042776 * A031212 A165133 A044217
KEYWORD
nonn,frac,easy
EXTENSIONS
More terms from Vincenzo Librandi, Dec 04 2013
STATUS
approved