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A042023 Denominators of continued fraction convergents to sqrt(535). 2
1, 7, 8, 23, 100, 123, 469, 592, 2837, 6266, 9103, 69987, 3228505, 22669522, 25898027, 74465576, 323760331, 398225907, 1518438052, 1916663959, 9185093888, 20286851735, 29471945623, 226590471096, 10452633616039, 73395025783369, 83847659399408, 241090344582185 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3237608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

FORMULA

G.f.: -(x^22 -7*x^21 +8*x^20 -23*x^19 +100*x^18 -123*x^17 +469*x^16 -592*x^15 +2837*x^14 -6266*x^13 +9103*x^12 -69987*x^11 -9103*x^10 -6266*x^9 -2837*x^8 -592*x^7 -469*x^6 -123*x^5 -100*x^4 -23*x^3 -8*x^2 -7*x -1)/(x^24 -3237608*x^12 +1). - Vincenzo Librandi, Jan 12 2014

a(n) = 3237608*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Jan 12 2014

MATHEMATICA

Denominator[Convergents[Sqrt[535], 30]] (* or *) CoefficientList[Series[-(x^22 - 7 x^21 + 8 x^20 - 23 x^19 + 100 x^18 - 123 x^17 + 469 x^16 - 592 x^15 + 2837 x^14 - 6266 x^13 + 9103 x^12 - 69987 x^11 - 9103 x^10 -6266 x^9 - 2837 x^8 - 592 x^7 - 469 x^6 - 123 x^5 - 100 x^4 - 23 x^3 - 8 x^2 - 7 x - 1)/(x^24 - 3237608 x^12 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Jan 12 2014 *)

PROG

(MAGMA) I:=[1, 7, 8, 23, 100, 123, 469, 592, 2837, 6266, 9103, 69987, 3228505, 22669522, 25898027, 74465576, 323760331, 398225907, 1518438052, 1916663959, 9185093888, 20286851735, 29471945623, 226590471096]; [n le 24 select I[n] else 3237608*Self(n-12)-Self(n-24): n in [1..30]]; // Vincenzo Librandi, Jan 12 2014

CROSSREFS

Cf. A042022.

Sequence in context: A295337 A041104 A042391 * A041102 A136116 A080982

Adjacent sequences:  A042020 A042021 A042022 * A042024 A042025 A042026

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Jan 12 2014

STATUS

approved

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Last modified February 23 00:18 EST 2019. Contains 320411 sequences. (Running on oeis4.)