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A042885 Denominators of continued fraction convergents to sqrt(974). 2
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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A308485 A234143 A217686 * A042085 A136211 A041036
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Jan 31 2014
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)