A041437 Denominators of continued fraction convergents to sqrt(234).

1, 3, 7, 10, 27, 37, 101, 340, 10301, 31243, 72787, 104030, 280847, 384877, 1050601, 3536680, 107151001, 324989683, 757130367, 1082120050, 2921370467, 4003490517, 10928351501, 36788545020, 1114584702101, 3380542651323, 7875670004747, 11256212656070

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,10402,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -3*x^13 +7*x^12 -10*x^11 +27*x^10 -37*x^9 +101*x^8 -340*x^7 -101*x^6 -37*x^5 -27*x^4 -10*x^3 -7*x^2 -3*x -1) / ((x^4 -10*x^2 -1)*(x^4 +10*x^2 -1)*(x^8 +102*x^4 +1)). - Colin Barker, Nov 17 2013

a(n) = 10402*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 17 2013

Mathematica

Denominator[Convergents[Sqrt[234], 30]] (* Harvey P. Dale, Oct 03 2011 *)
CoefficientList[Series[-(x^14 - 3 x^13 + 7 x^12 - 10 x^11 + 27 x^10 - 37 x^9 + 101 x^8 - 340 x^7 - 101 x^6 - 37 x^5 - 27 x^4 - 10 x^3 - 7 x^2 - 3 x - 1)/((x^4 - 10 x^2 - 1) (x^4 + 10 x^2 - 1) (x^8 + 102 x^4 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 17 2013 *)

Prog

(Magma) I:=[1, 3, 7, 10, 27, 37, 101, 340, 10301, 31243, 72787, 104030, 280847, 384877, 1050601, 3536680]; [n le 16 select I[n] else 10402*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013

Crossrefs

Cf. A041436, A040218.

Sequence in context: A127277 A302704 A235490 * A302279 A041525 A251862

Adjacent sequences: A041434 A041435 A041436 * A041438 A041439 A041440

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 17 2013

Status

approved