A042885 - OEIS

%I #22 Jun 26 2022 23:47:34

%S 1,4,5,19,24,43,67,780,847,5015,15892,132151,148043,280194,428237,

%T 708431,21681167,22389598,44070765,66460363,110531128,950709387,

%U 2962659289,15764005832,18726665121,221757322163,240483987284,462241309447,702725296731,2570417199640

%N Denominators of continued fraction convergents to sqrt(974).

%H Andy Huchala, <a href="/A042885/b042885.txt">Table of n, a(n) for n = 0..2134</a> (first 201 terms from Vincenzo Librandi)

%H <a href="/index/Rec#order_64">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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 977651490470430, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F a(n) = 977651490470430*a(n-32) - a(n-64) for n > 63. - _Vincenzo Librandi_, Jan 31 2014

%F G.f.: p/q with p,q given in Sage program. - _Andy Huchala_, Mar 06 2022

%t Denominator[Convergents[Sqrt[974], 30]] (* _Harvey P. Dale_, Feb 07 2012 *)

%o (Sage)

%o R.<x> = PowerSeriesRing(ZZ,100)

%o p = -x^62 + 4*x^61 - 5*x^60 + 19*x^59 - 24*x^58 + 43*x^57 - 67*x^56 + 780*x^55 - 847*x^54 + 5015*x^53 - 15892*x^52 + 132151*x^51 - 148043*x^50 + 280194*x^49 - 428237*x^48 + 708431*x^47 - 21681167*x^46 + 22389598*x^45 - 44070765*x^44 + 66460363*x^43 - 110531128*x^42 + 950709387*x^41 - 2962659289*x^40 + 15764005832*x^39 - 18726665121*x^38 + 221757322163*x^37 - 240483987284*x^36 + 462241309447*x^35 - 702725296731*x^34 + 2570417199640*x^33 - 3273142496371*x^32 + 15662987185124*x^31 + 3273142496371*x^30 + 2570417199640*x^29 + 702725296731*x^28 + 462241309447*x^27 + 240483987284*x^26 + 221757322163*x^25 + 18726665121*x^24 + 15764005832*x^23 + 2962659289*x^22 + 950709387*x^21 + 110531128*x^20 + 66460363*x^19 + 44070765*x^18 + 22389598*x^17 + 21681167*x^16 + 708431*x^15 + 428237*x^14 + 280194*x^13 + 148043*x^12 + 132151*x^11 + 15892*x^10 + 5015*x^9 + 847*x^8 + 780*x^7 + 67*x^6 + 43*x^5 + 24*x^4 + 19*x^3 + 5*x^2 + 4*x + 1

%o q = x^64 - 977651490470430*x^32 + 1

%o (p/q).list() # _Andy Huchala_, Mar 06 2022

%Y Cf. A042884, A040942.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Vincenzo Librandi_, Jan 31 2014