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A042086 Numerators of continued fraction convergents to sqrt(567). 2
23, 24, 119, 381, 1643, 2024, 94747, 96771, 481831, 1542264, 6650887, 8193151, 383535833, 391728984, 1950451769, 6243084291, 26922788933, 33165873224, 1552552957237, 1585718830461, 7895428279081 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,4048,0,0,0,0,0,-1).
FORMULA
G.f.: -(x^11 - 23*x^10 + 24*x^9 - 119*x^8 + 381*x^7 - 1643*x^6 - 2024*x^5 - 1643*x^4 - 381*x^3 - 119*x^2 - 24*x - 23)/(x^12 - 4048*x^6 + 1). - Vincenzo Librandi, Nov 16 2013
a(n) = 4048*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 16 2013
MATHEMATICA
Numerator[Convergents[Sqrt[567], 30]] (* or *) CoefficientList[Series[-(x^11 - 23 x^10 + 24 x^9 - 119 x^8 + 381 x^7 - 1643 x^6 - 2024 x^5 - 1643 x^4 - 381 x^3 - 119 x^2 - 24 x - 23)/(x^12 - 4048 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)
PROG
(Magma) I:=[23, 24, 119, 381, 1643, 2024, 94747, 96771, 481831, 1542264, 6650887, 8193151]; [n le 12 select I[n] else 4048*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013
CROSSREFS
Cf. A042087.
Sequence in context: A042084 A042082 A042088 * A042090 A042092 A042094
KEYWORD
nonn,cofr,frac,easy,less
AUTHOR
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)