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A042896 Numerators of continued fraction convergents to sqrt(980). 2

%I

%S 31,94,313,407,720,1847,2567,4414,15809,51841,3229951,9741694,

%T 32455033,42196727,74651760,191500247,266152007,457652254,1639108769,

%U 5374978561,334887779551,1010038317214,3365002731193,4375041048407,7740043779600,19855128607607,27595172387207,47450300994814,169946075371649

%N Numerators of continued fraction convergents to sqrt(980).

%H Vincenzo Librandi, <a href="/A042896/b042896.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 103682, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F 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

%F a(n) = 103682*a(n-10) - a(n-20). - _Vincenzo Librandi_, Dec 08 2013

%t 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 *)

%o (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

%Y Cf. A042897.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Dec 08 2013

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Last modified August 7 23:38 EDT 2020. Contains 336279 sequences. (Running on oeis4.)