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 A041621 Denominators of continued fraction convergents to sqrt(329). 2

%I

%S 1,7,29,65,94,159,730,889,1619,4127,18127,131016,4734703,33273937,

%T 137830451,308934839,446765290,755700129,3469565806,4225265935,

%U 7694831741,19614929417,86154549409,622696775280,22503238459489,158145365991703,655084702426301

%N Denominators of continued fraction convergents to sqrt(329).

%H Vincenzo Librandi, <a href="/A041621/b041621.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, 4752830, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f. (1 +7*x +29*x^2 +65*x^3 +94*x^4 +159*x^5 +730*x^6 +889*x^7 +1619*x^8 +4127*x^9 +18127*x^10 +131016*x^11 -18127*x^12 +4127*x^13 -1619*x^14 +889*x^15 -730*x^16 +159*x^17 -94*x^18 +65*x^19 -29*x^20 +7*x^21 -x^22)/(1 -4752830*x^12 +x^24). - _Vincenzo Librandi_, Dec 22 2013

%F a(n) = 4752830*a(n-12) - a(n-24) for n>23. - _Vincenzo Librandi_, Dec 22 2013

%t Denominator[Convergents[Sqrt[329], 30]] (* or *) CoefficientList[Series[(1 + 7 x + 29 x^2 + 65 x^3 + 94 x^4 + 159 x^5 + 730 x^6 + 889 x^7 + 1619 x^8 + 4127 x^9 + 18127 x^10 + 131016 x^11 - 18127 x^12 + 4127 x^13 - 1619 x^14 + 889 x^15 - 730 x^16 + 159 x^17 - 94 x^18 + 65 x^19 - 29 x^20 + 7 x^21 - x^22)/(1 - 4752830 x^12 + x^24), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 22 2013 *)

%o (Magma) I:= 1,7,29,65,94,159,730,889,1619,4127,18127, 131016,4734703,33273937,137830451,308934839,446765290, 755700129,3469565806,4225265935,7694831741,19614929417, 86154549409,622696775280]; [n le 24 select I[n] else 4752830*Self(n-12)-Self(n-24): n in [1..40]]; // _Vincenzo Librandi_, Dec 22 2013

%Y Cf. A041620.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Dec 22 2013

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Last modified December 2 11:37 EST 2022. Contains 358493 sequences. (Running on oeis4.)