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A042416
Numerators of continued fraction convergents to sqrt(736).
2
27, 190, 217, 624, 841, 2306, 3147, 24335, 1317237, 9244994, 10562231, 30369456, 40931687, 112232830, 153164517, 1184384449, 64109924763, 449953857790, 514063782553, 1478081422896, 1992145205449
OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,48670,0,0,0,0,0,0,0,-1).
FORMULA
G.f.: -(x^15 -27*x^14 +190*x^13 -217*x^12 +624*x^11 -841*x^10 +2306*x^9 -3147*x^8 -24335*x^7 -3147*x^6 -2306*x^5 -841*x^4 -624*x^3 -217*x^2 -190*x -27)/(x^16 -48670*x^8 +1). - Vincenzo Librandi, Nov 23 2013
a(n) = 48670*a(n-8) - a(n-16). - Vincenzo Librandi, Nov 23 2013
MATHEMATICA
Numerator[Convergents[Sqrt[736], 30]] (* or *) CoefficientList[Series[-(x^15 - 27 x^14 + 190 x^13 - 217 x^12 + 624 x^11 - 841 x^10 + 2306 x^9 - 3147 x^8 - 24335 x^7 - 3147 x^6 - 2306 x^5 - 841 x^4 - 624 x^3 - 217 x^2 - 190 x - 27)/(x^16 - 48670 x^8 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 23 2013 *)
PROG
(Magma) I:=[27, 190, 217, 624, 841, 2306, 3147, 24335, 1317237, 9244994, 10562231, 30369456, 40931687, 112232830, 153164517, 1184384449]; [n le 16 select I[n] else 48670*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Nov 23 2013
CROSSREFS
Cf. A042417.
Sequence in context: A000499 A365890 A365884 * A216108 A216110 A216112
KEYWORD
nonn,cofr,frac,easy
STATUS
approved