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A042885
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Denominators of continued fraction convergents to sqrt(974).
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2
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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
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OFFSET
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0,2
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LINKS
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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).
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FORMULA
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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
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MATHEMATICA
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Denominator[Convergents[Sqrt[974], 30]] (* Harvey P. Dale, Feb 07 2012 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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