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Search: a042048 -id:a042048
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Denominators of continued fraction convergents to sqrt(548).
+10
2
1, 2, 5, 17, 22, 127, 149, 1617, 1766, 10447, 12213, 47086, 106385, 259856, 12059761, 24379378, 60818517, 206834929, 267653446, 1545102159, 1812755605, 19672658209, 21485413814, 127099727279, 148585141093, 572855150558, 1294295442209, 3161446034976
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12166146, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^26 -2*x^25 +5*x^24 -17*x^23 +22*x^22 -127*x^21 +149*x^20 -1617*x^19 +1766*x^18 -10447*x^17 +12213*x^16 -47086*x^15 +106385*x^14 -259856*x^13 -106385*x^12 -47086*x^11 -12213*x^10 -10447*x^9 -1766*x^8 -1617*x^7 -149*x^6 -127*x^5 -22*x^4 -17*x^3 -5*x^2 -2*x -1)/(x^28 -12166146*x^14 +1). - Vincenzo Librandi, Jan 13 2014
a(n) = 12166146*a(n-14) - a(n-28) for n>27. - Vincenzo Librandi, Jan 13 2014
MATHEMATICA
Denominator[Convergents[Sqrt[548], 30]] (* or *) CoefficientList[Series[-(x^26 - 2 x^25 + 5 x^24 - 17 x^23 + 22 x^22 - 127 x^21 + 149 x^20 - 1617 x^19 + 1766 x^18 - 10447 x^17 + 12213 x^16 - 47086 x^15 + 106385 x^14 - 259856 x^13 - 106385 x^12 - 47086 x^11 - 12213 x^10 - 10447 x^9 - 1766 x^8 - 1617 x^7 - 149 x^6 - 127 x^5 - 22 x^4 - 17 x^3 - 5 x^2 - 2 x - 1)/(x^28 - 12166146 x^14 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Jan 13 2014 *)
PROG
(Magma) I:=[1, 2, 5, 17, 22, 127, 149, 1617, 1766, 10447, 12213, 47086, 106385, 259856, 12059761, 24379378, 60818517, 206834929, 267653446, 1545102159, 1812755605, 19672658209, 21485413814, 127099727279, 148585141093, 572855150558, 1294295442209, 3161446034976]; [n le 28 select I[n] else 12166146*Self(n-14)-Self(n-28): n in [1..30]]; // Vincenzo Librandi, Jan 13 2014
CROSSREFS
Cf. A042048.
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Jan 13 2014
STATUS
approved

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