A042244 - OEIS

%I #14 Sep 08 2022 08:44:55

%S 25,51,280,1731,8935,19601,988985,1997571,10976840,67858611,350269895,

%T 768398401,38770189945,78308778291,430314081400,2660193266691,

%U 13731280414855,30122754096401,1519868985234905

%N Numerators of continued fraction convergents to sqrt(648).

%H Vincenzo Librandi, <a href="/A042244/b042244.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,39202,0,0,0,0,0,-1).

%F G.f.: (25 + 51*x + 280*x^2 + 1731*x^3 + 8935*x^4 + 19601*x^5 + 8935*x^6 - 1731*x^7 + 280*x^8 - 51*x^9 + 25*x^10 - x^11)/(1 - 39202*x^6 + x^12). - _Vincenzo Librandi_, Nov 19 2013

%F a(n) = 39202*a(n-6) - a(n-12). - _Vincenzo Librandi_, Nov 19 2013

%t Numerator[Convergents[Sqrt[648], 30]] (* or *) CoefficientList[Series[(25 + 51 x + 280 x^2 + 1731 x^3 + 8935 x^4 + 19601 x^5 + 8935 x^6 - 1731 x^7 + 280 x^8 - 51 x^9 + 25 x^10 - x^11)/(1 - 39202 x^6 + x^12), {x, 0, 20}], x] (* _Vincenzo Librandi_, Nov 19 2013 *)

%o (Magma) I:=[25,51,280,1731,8935,19601,988985,1997571,10976840,67858611, 350269895,768398401]; [n le 12 select I[n] else 39202*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Nov 19 2013

%Y Cf. A042245.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.