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A042672
Numerators of continued fraction convergents to sqrt(866).
2
29, 59, 147, 206, 5915, 6121, 18157, 42435, 2479387, 5001209, 12481805, 17483014, 502006197, 519489211, 1540984619, 3601458449, 210425574661, 424452607771, 1059330790203, 1483783397974, 42605265933475, 44089049331449, 130783364596373, 305655778524195
OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 84870, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: (29 +59*x +147*x^2 +206*x^3 +5915*x^4 +6121*x^5 +18157*x^6 +42435*x^7 +18157*x^8 -6121*x^9 +5915*x^10 -206*x^11 +147*x^12 -59*x^13 +29*x^14 -x^15)/(1 -84870*x^8 +x^16). - Vincenzo Librandi, Dec 01 2013
a(n) = 84870*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 01 2013
MATHEMATICA
Numerator[Convergents[Sqrt[866], 30]] (* or *) CoefficientList[Series[(29 + 59 x + 147 x^2 + 206 x^3 + 5915 x^4 + 6121 x^5 + 18157 x^6 + 42435 x^7 + 18157 x^8 - 6121 x^9 + 5915 x^10 - 206 x^11 + 147 x^12 - 59 x^13 + 29 x^14 - x^15)/(1 - 84870 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 30 2013 *)
PROG
(Magma) I:=[29, 59, 147, 206, 5915, 6121, 18157, 42435, 2479387, 5001209, 12481805, 17483014, 502006197, 519489211, 1540984619, 3601458449]; [n le 16 select I[n] else 84870*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Dec 01 2013
CROSSREFS
Cf. A042673.
Sequence in context: A140754 A047078 A073651 * A042670 A129813 A060229
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved