A042398 - OEIS

%I #17 Nov 27 2022 13:09:12

%S 26,27,458,485,25678,26163,444286,470449,24907634,25378083,430956962,

%T 456335045,24160379302,24616714347,418027808854,442644523201,

%U 23435543015306,23878187538507,405486543631418

%N Numerators of continued fraction convergents to sqrt(726).

%H Vincenzo Librandi, <a href="/A042398/b042398.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 970, 0, 0, 0, -1).

%F G.f.: (26+27* x+458* x^2+485*x^3+458*x^4-27*x^5+26*x^6-x^7)/(1-970*x^4+x^8). - _Vincenzo Librandi_, Nov 23 2013

%F a(n) = 970*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 23 2013

%t Numerator[Convergents[Sqrt[726], 30]] (* or *) CoefficientList[Series[(26 + 27 x + 458 x^2 + 485 x^3 + 458 x^4 - 27 x^5 + 26 x^6 - x^7)/(1 - 970 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 23 2013 *)

%t LinearRecurrence[{0,0,0,970,0,0,0,-1},{26,27,458,485,25678,26163,444286,470449},30] (* _Harvey P. Dale_, Nov 27 2022 *)

%o (Magma) I:=[26, 27, 458, 485, 25678, 26163, 444286, 470449]; [n le 8 select I[n] else 970*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 23 2013

%Y Cf. A042399.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.