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Numerators of continued fraction convergents to sqrt(449).
2

%I #15 Nov 14 2021 10:35:05

%S 21,106,339,445,784,1229,9387,10616,62467,322951,385418,3020877,

%T 3406295,6427172,9833467,35927573,189471332,7993723517,40158088917,

%U 128467990268,168626079185,297094069453,465720148638

%N Numerators of continued fraction convergents to sqrt(449).

%H Vincenzo Librandi, <a href="/A041854/b041854.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_34">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 378942664, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

%F a(n) = 378942664*a(n-17) + a(n-34) for n>33. [_Bruno Berselli_, Nov 10 2013]

%t Numerator[Convergents[Sqrt[449], 30]] (* _Vincenzo Librandi_, Nov 10 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,378942664,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1},{21,106,339,445,784,1229,9387,10616,62467,322951,385418,3020877,3406295,6427172,9833467,35927573,189471332,7993723517,40158088917,128467990268,168626079185,297094069453,465720148638,3557135109919,4022855258557,23671411402704,122379912272077,146051323674781,1144739177995544,1290790501670325,2435529679665869,3726320181336194,13614490223674451,71798771299708449},30] (* _Harvey P. Dale_, Nov 14 2021 *)

%Y Cf. A041855.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.