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A041286
Numerators of continued fraction convergents to sqrt(156).
3
12, 25, 612, 1249, 30588, 62425, 1528788, 3120001, 76408812, 155937625, 3818911812, 7793761249, 190869181788, 389532124825, 9539640177588, 19468812480001, 476791139697612, 973051091875225, 23830017344703012
OFFSET
0,1
FORMULA
G.f.: (12+25*x+12*x^2-x^3)/(1-50*x^2+x^4). - Vincenzo Librandi, Nov 01 2013
a(n) = 50*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 01 2013
a(n) = (12 + sqrt(13) + (12 - sqrt(13))*(-1)^n)*cosh(n*arccosh(25)/2)/2 + sqrt(3)*(1 + sqrt(13) + (sqrt(13) - 1)*(-1)^n)*sinh(n*arccosh(25)/2). - Stefano Spezia, Jul 05 2022
MATHEMATICA
Numerator[Convergents[Sqrt[156], 30]] (* or *) CoefficientList[Series[(12 + 25 x + 12 x^2 - x^3)/(1 - 50 x^2 + x^4), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 01 2013 *)
PROG
(Magma) I:=[12, 25, 612, 1249]; [n le 4 select I[n] else 50*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 01 2013
CROSSREFS
Sequence in context: A041284 A171069 A042193 * A025138 A075689 A054303
KEYWORD
nonn,cofr,frac,easy
STATUS
approved