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A042656
Numerators of continued fraction convergents to sqrt(858).
2
29, 88, 205, 703, 40979, 123640, 288259, 988417, 57616445, 173837752, 405291949, 1389713599, 81008680691, 244415755672, 569840192035, 1953936331777, 113898147435101, 343648378637080, 801194904709261
OFFSET
0,1
LINKS
FORMULA
G.f.: (29 +88*x +205*x^2 +703*x^3 +205*x^4 -88*x^5 +29*x^6 -x^7)/(1 -1406*x^4 +x^8). - Vincenzo Librandi, Nov 30 2013
a(n) = 1406*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 30 2013
MATHEMATICA
Numerator[Convergents[Sqrt[858], 30]] (* or *) CoefficientList[Series[(29 + 88 x + 205 x^2 + 703 x^3 + 205 x^4 - 88 x^5 + 29 x^6 - x^7)/(1 - 1406 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 30 2013 *)
LinearRecurrence[{0, 0, 0, 1406, 0, 0, 0, -1}, {29, 88, 205, 703, 40979, 123640, 288259, 988417}, 20] (* Harvey P. Dale, Mar 01 2019 *)
PROG
(Magma) I:=[29, 88, 205, 703, 40979, 123640, 288259, 988417]; [n le 8 select I[n] else 1406*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 30 2013
CROSSREFS
Cf. A042657.
Sequence in context: A032508 A042654 A042652 * A042658 A042660 A047650
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved