A042023 Denominators of continued fraction convergents to sqrt(535).

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

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 A329635

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