A042885 Denominators of continued fraction convergents to sqrt(974).

1, 4, 5, 19, 24, 43, 67, 780, 847, 5015, 15892, 132151, 148043, 280194, 428237, 708431, 21681167, 22389598, 44070765, 66460363, 110531128, 950709387, 2962659289, 15764005832, 18726665121, 221757322163, 240483987284, 462241309447, 702725296731, 2570417199640

Offset

0,2

Links

Andy Huchala, Table of n, a(n) for n = 0..2134 (first 201 terms from Vincenzo Librandi)

Index entries for linear recurrences with constant coefficients, 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).

Formula

a(n) = 977651490470430*a(n-32) - a(n-64) for n > 63. - Vincenzo Librandi, Jan 31 2014

G.f.: p/q with p,q given in Sage program. - Andy Huchala, Mar 06 2022

Mathematica

Denominator[Convergents[Sqrt[974], 30]] (* Harvey P. Dale, Feb 07 2012 *)

Prog

(Sage)
R.<x> = PowerSeriesRing(ZZ, 100)
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
q = x^64 - 977651490470430*x^32 + 1
(p/q).list() # Andy Huchala, Mar 06 2022

Crossrefs

Cf. A042884, A040942.

Sequence in context: A308485 A234143 A217686 * A042085 A136211 A041036

Adjacent sequences: A042882 A042883 A042884 * A042886 A042887 A042888

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Jan 31 2014

Status

approved