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A042748 Numerators of continued fraction convergents to sqrt(905). 2
30, 361, 21690, 260641, 15660150, 188182441, 11306606610, 135867461761, 8163354312270, 98096119209001, 5893930506852330, 70825262201436961, 4255409662593069990, 51135741213318276841, 3072399882461689680450 (list; graph; refs; listen; history; text; internal format)
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, 722, 0, -1).

FORMULA

G.f.: (30 +361*x +30*x^2 -x^3)/(1 -722*x^2 +x^4). - Vincenzo Librandi, Dec 03 2013

a(n) = 722*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 03 2013

MATHEMATICA

Numerator[Convergents[Sqrt[905], 30]] (* or *) CoefficientList[Series[(30 + 361 x + 30 x^2 - x^3)/(1 - 722 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2013 *)

PROG

(MAGMA) I:=[30, 361, 21690, 260641]; [n le 4 select I[n] else 722*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 03 2013

CROSSREFS

Cf. A042749.

Sequence in context: A086864 A138441 A058837 * A202074 A251895 A022690

Adjacent sequences:  A042745 A042746 A042747 * A042749 A042750 A042751

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 2 08:31 EST 2021. Contains 349437 sequences. (Running on oeis4.)