A041872 - OEIS

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A041872

Numerators of continued fraction convergents to sqrt(458).

21, 43, 107, 4537, 9181, 22899, 970939, 1964777, 4900493, 207785483, 420471459, 1048728401, 44467064301, 89982857003, 224432778307, 9516159545897, 19256751870101, 48029663286099, 2036502609886259

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OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,214,0,0,1).

FORMULA

G.f.: (21 + 43*x + 107*x^2 + 43*x^3 - 21*x^4 + x^5)/(1 - 214*x^3 - x^6). [Bruno Berselli, Nov 11 2013]

a(n) = 214*a(n-3) + a(n-6) for n>5. [Bruno Berselli, Nov 11 2013]

MATHEMATICA

Numerator[Convergents[Sqrt[458], 20]] (* Harvey P. Dale, Aug 26 2013 *)

LinearRecurrence[{0, 0, 214, 0, 0, 1}, {21, 43, 107, 4537, 9181, 22899}, 30] (* Bruno Berselli, Nov 11 2013 *)