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Numerators of continued fraction convergents to sqrt(108).
2

%I #14 Jul 26 2024 15:23:25

%S 10,21,31,52,239,291,530,1351,27550,56451,84001,140452,645809,786261,

%T 1432070,3650401,74440090,152530581,226970671,379501252,1744975679,

%U 2124476931,3869452610,9863382151,201137095630,412137573411,613274669041,1025412242452

%N Numerators of continued fraction convergents to sqrt(108).

%H Vincenzo Librandi, <a href="/A041194/b041194.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 (0,0,0,0,0,0,0,2702,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^15 -10*x^14 +21*x^13 -31*x^12 +52*x^11 -239*x^10 +291*x^9 -530*x^8 -1351*x^7 -530*x^6 -291*x^5 -239*x^4 -52*x^3 -31*x^2 -21*x -10) / ((x^8 -52*x^4 +1)*(x^8 +52*x^4 +1)). - _Colin Barker_, Nov 05 2013

%t Numerator[Convergents[Sqrt[108], 30]] (* _Vincenzo Librandi_, Oct 30 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,2702,0,0,0,0,0,0,0,-1},{10,21,31,52,239,291,530,1351,27550,56451,84001,140452,645809,786261,1432070,3650401},30] (* _Harvey P. Dale_, Jul 26 2024 *)

%Y Cf. A041195.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 05 2013