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A041075
Denominators of continued fraction convergents to sqrt(44).
2
1, 1, 2, 3, 8, 11, 19, 30, 379, 409, 788, 1197, 3182, 4379, 7561, 11940, 150841, 162781, 313622, 476403, 1266428, 1742831, 3009259, 4752090, 60034339, 64786429, 124820768, 189607197, 504035162, 693642359, 1197677521, 1891319880, 23893516081, 25784835961
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,398,0,0,0,0,0,0,0,-1).
FORMULA
G.f.: -(x^2-x-1)*(x^4+3*x^2+1)*(x^8+10*x^4+1) / ((x^8-20*x^4+1)*(x^8+20*x^4+1)). - Colin Barker, Nov 12 2013
a(n) = 398*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 11 2013
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[44], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011 *)
Denominator[Convergents[Sqrt[44], 30]] (* Vincenzo Librandi, Dec 11 2013 *)
PROG
(Magma) I:=[1, 1, 2, 3, 8, 11, 19, 30, 379, 409, 788, 1197, 3182, 4379, 7561, 11940]; [n le 16 select I[n] else 398*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013
CROSSREFS
Sequence in context: A291202 A091076 A112595 * A041893 A206241 A295333
KEYWORD
nonn,cofr,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 12 2013
STATUS
approved