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A042042 Numerators of continued fraction convergents to sqrt(545). 2
23, 47, 70, 607, 677, 1961, 90883, 183727, 274610, 2380607, 2655217, 7691041, 356443103, 720577247, 1077020350, 9336740047, 10413760397, 30164260841, 1397969759083, 2826103779007, 4224073538090 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 3922, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: (23 +47*x +70*x^2 +607*x^3 +677*x^4 +1961*x^5 +677*x^6 -607*x^7 +70*x^8 -47*x^9 +23*x^10 -x^11) / (1 -3922*x^6 +x^12). - Vincenzo Librandi, Nov 13 2013
a(n) = 3922*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 14 2013
MATHEMATICA
Numerator[Convergents[Sqrt[545], 30]] (* Harvey P. Dale, Oct 28 2012 *)
CoefficientList[Series[(23 + 47 x + 70 x^2 + 607 x^3 + 677 x^4 + 1961 x^5 + 677 x^6 - 607 x^7 + 70 x^8 - 47 x^9 + 23 x^10 - x^11)/(1 - 3922 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 13 2013 *)
PROG
(Magma) I:=[23, 47, 70, 607, 677, 1961, 90883, 183727, 274610, 2380607, 2655217, 7691041]; [n le 12 select I[n] else 3922*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 14 2013
CROSSREFS
Cf. A042043.
Sequence in context: A244092 A042046 A042044 * A130063 A183010 A134517
KEYWORD
nonn,cofr,frac,easy,less
AUTHOR
STATUS
approved

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Last modified June 13 23:50 EDT 2024. Contains 373391 sequences. (Running on oeis4.)