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A041323
Denominators of continued fraction convergents to sqrt(175).
2
1, 4, 9, 13, 35, 153, 4013, 16205, 36423, 52628, 141679, 619344, 16244623, 65597836, 147440295, 213038131, 573516557, 2507104359, 65758229891, 265540023923, 596838277737, 862378301660, 2321594881057, 10148757825888, 266189298354145, 1074905951242468
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,4048,0,0,0,0,0,-1).
FORMULA
G.f.: -(x^10 -4*x^9 +9*x^8 -13*x^7 +35*x^6 -153*x^5 -35*x^4 -13*x^3 -9*x^2 -4*x -1) / ((x^4 -16*x^2 +1)*(x^8 +16*x^6 +255*x^4 +16*x^2 +1)). - Colin Barker, Nov 15 2013
a(n) = 4048*a(n-6) - a(n-12). - Vincenzo Librandi, Dec 15 2013
MATHEMATICA
Denominator[Convergents[Sqrt[175], 30]] (* Vincenzo Librandi, Dec 15 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 4048, 0, 0, 0, 0, 0, -1}, {1, 4, 9, 13, 35, 153, 4013, 16205, 36423, 52628, 141679, 619344}, 30] (* Harvey P. Dale, Jan 11 2024 *)
PROG
(Magma) I:=[1, 4, 9, 13, 35, 153, 4013, 16205, 36423, 52628, 141679, 619344]; [n le 12 select I[n] else 4048*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013
CROSSREFS
Sequence in context: A333848 A063606 A033287 * A319217 A041028 A041211
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 15 2013
STATUS
approved