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A042896 Numerators of continued fraction convergents to sqrt(980). 2
31, 94, 313, 407, 720, 1847, 2567, 4414, 15809, 51841, 3229951, 9741694, 32455033, 42196727, 74651760, 191500247, 266152007, 457652254, 1639108769, 5374978561, 334887779551, 1010038317214, 3365002731193, 4375041048407, 7740043779600, 19855128607607, 27595172387207, 47450300994814, 169946075371649 (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, 0, 0, 0, 0, 0, 0, 0, 0, 103682, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

FORMULA

G.f.: (31 +94*x +313*x^2 +407*x^3 +720*x^4 +1847*x^5 +2567*x^6 +4414*x^7 +15809*x^8 +51841*x^9 +15809*x^10 -4414*x^11 +2567*x^12 -1847*x^13 +720*x^14 -407*x^15 +313*x^16 -94*x^17 +31*x^18 -x^19) / (1 -103682*x^10 +x^20). - Vincenzo Librandi, Dec 08 2013

a(n) = 103682*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 08 2013

MATHEMATICA

Numerator[Convergents[Sqrt[980], 30]] (* or *) CoefficientList[Series[(31 + 94 x + 313 x^2 + 407 x^3 + 720 x^4 + 1847 x^5 + 2567 x^6+4414 x^7 + 15809 x^8 + 51841 x^9 + 15809 x^10 - 4414 x^11 + 2567 x^12 - 1847 x^13 + 720 x^14 - 407 x^15 + 313 x^16 - 94 x^17 + 31 x^18 - x^19) / (1 - 103682 x^10 + x^20), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 08 2013 *)

PROG

(MAGMA) I:=[31, 94, 313, 407, 720, 1847, 2567, 4414, 15809, 51841, 3229951, 9741694, 32455033, 42196727, 74651760, 191500247, 266152007, 457652254, 1639108769, 5374978561]; [n le 20 select I[n] else 103682*Self(n-10)-Self(n-20): n in [1..30]]; // Vincenzo Librandi, Dec 08 2013

CROSSREFS

Cf. A042897.

Sequence in context: A042892 A042890 A042894 * A042898 A044218 A044599

Adjacent sequences:  A042893 A042894 A042895 * A042897 A042898 A042899

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Dec 08 2013

STATUS

approved

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Last modified March 20 13:18 EDT 2019. Contains 321345 sequences. (Running on oeis4.)