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A041437 Denominators of continued fraction convergents to sqrt(234). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Sequence in context: A127277 A302704 A235490 * A302279 A041525 A251862
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 17 2013
STATUS
approved

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Last modified June 20 22:36 EDT 2024. Contains 373532 sequences. (Running on oeis4.)