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A041209
Denominators of continued fraction convergents to sqrt(115).
2
1, 1, 3, 4, 7, 11, 18, 29, 76, 105, 2176, 2281, 6738, 9019, 15757, 24776, 40533, 65309, 171151, 236460, 4900351, 5136811, 15173973, 20310784, 35484757, 55795541, 91280298, 147075839, 385431976, 532507815, 11035588276, 11568096091, 34171780458, 45739876549
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,2252,0,0,0,0,0,0,0,0,0,-1).
FORMULA
G.f.: -(x^2-x-1)*(x^16+4*x^14+11*x^12+29*x^10+105*x^8+29*x^6+11*x^4+4*x^2+1) / (x^20-2252*x^10+1). - Colin Barker, Nov 14 2013
a(n) = 2252*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 13 2013
MATHEMATICA
Denominator[Convergents[Sqrt[115], 30]] (* Harvey P. Dale, Oct 22 2012 *)
CoefficientList[Series[-(x^2 - x - 1) (x^16 + 4 x^14 + 11 x^12 + 29 x^10 + 105 x^8 + 29 x^6 + 11 x^4 + 4 x^2 + 1)/(x^20 - 2252 x^10 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 13 2013 *)
PROG
(Magma) I:=[1, 1, 3, 4, 7, 11, 18, 29, 76, 105, 2176, 2281, 6738, 9019, 15757, 24776, 40533, 65309, 171151, 236460]; [n le 20 select I[n] else 2252*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013
CROSSREFS
Sequence in context: A358995 A042433 A024319 * A293420 A041739 A042593
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 14 2013
STATUS
approved