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Numerators of continued fraction convergents to sqrt(403).
2

%I #19 Mar 18 2017 12:56:26

%S 20,261,542,803,2951,3754,14213,17967,50147,669878,26845267,349658349,

%T 726161965,1075820314,3953622907,5029443221,19041952570,24071395791,

%U 67184744152,897473069767,35966107534832,468456871022583,972879849579998,1441336720602581

%N Numerators of continued fraction convergents to sqrt(403).

%H Vincenzo Librandi, <a href="/A041764/b041764.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, 1339756, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F a(n) = 1339756*a(n-10) - a(n-20) for n>19. - _Bruno Berselli_, Nov 07 2013

%F G.f.: -(x^19 -20*x^18 +261*x^17 -542*x^16 +803*x^15 -2951*x^14 +3754*x^13 -14213*x^12 +17967*x^11 -50147*x^10 -669878*x^9 -50147*x^8 -17967*x^7 -14213*x^6 -3754*x^5 -2951*x^4 -803*x^3 -542*x^2 -261*x -20) / (x^20 -1339756*x^10 +1). - _Colin Barker_, Dec 28 2013

%t Numerator[Convergents[Sqrt[403], 30]] (* _Vincenzo Librandi_, Nov 07 2013 *)

%o (PARI) Vec(-(x^19-20*x^18+261*x^17-542*x^16+803*x^15-2951*x^14+3754*x^13-14213*x^12+17967*x^11-50147*x^10-669878*x^9-50147*x^8-17967*x^7-14213*x^6-3754*x^5-2951*x^4-803*x^3-542*x^2-261*x-20)/(x^20-1339756*x^10+1)+O(x^99)) \\ _Charles R Greathouse IV_, Jun 12 2015

%Y Cf. A041765, A040382.

%K nonn,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 28 2013