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Denominators of continued fraction convergents to sqrt(369).
2

%I #18 Feb 21 2018 12:54:49

%S 1,4,5,19,43,320,1323,9581,20485,71036,91521,437120,16702081,67245444,

%T 83947525,319088019,722123563,5373952960,22217935403,160899500781,

%U 344016936965,1192950311676,1536967248641,7340819306240,280488100885761,1129293222849284

%N Denominators of continued fraction convergents to sqrt(369).

%H Vincenzo Librandi, <a href="/A041699/b041699.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16793602, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: (1 +4*x +5*x^2 +19*x^3 +43*x^4 +320*x^5 +1323*x^6 +9581*x^7 +20485*x^8 +71036*x^9 +91521*x^10 +437120*x^11 -91521*x^12 +71036*x^13 -20485*x^14 +9581*x^15 -1323*x^16 +320*x^17 -43*x^18 +19*x^19 -5*x^20 +4*x^21 -x^22)/(1 -16793602*x^12 +x^24). - _Vincenzo Librandi_, Dec 23 2013

%F a(n) = 16793602*a(n-12) - a(n-24) for n>23. - _Vincenzo Librandi_, Dec 23 2013

%t Denominator[Convergents[Sqrt[369], 30]] (* or *) CoefficientList[Series[(1 + 4 x + 5 x^2 + 19 x^3 + 43 x^4 + 320 x^5 + 1323 x^6 + 9581 x^7 + 20485 x^8 + 71036 x^9 + 91521 x^10 + 437120 x^11 - 91521 x^12 + 71036 x^13 - 20485 x^14 + 9581 x^15 - 1323 x^16 + 320 x^17 - 43 x^18 + 19 x^19 - 5 x^20 + 4 x^21 - x^22)/(1 - 16793602 x^12 + x^24), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 23 2013 *)

%Y Cf. A041698.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Vincenzo Librandi_, Dec 23 2013