login
A041995
Denominators of continued fraction convergents to sqrt(520).
2
1, 1, 5, 56, 229, 285, 12769, 13054, 64985, 727889, 2976541, 3704430, 165971461, 169675891, 844675025, 9461101166, 38689079689, 48150180855, 2157297037309, 2205447218164, 10979085909965, 122975392227779, 502880654821081, 625856047048860
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 12998, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^10 -x^9 +5*x^8 -56*x^7 +229*x^6 -285*x^5 -229*x^4 -56*x^3 -5*x^2 -x -1) / ((x^6 -114*x^3 -1)*(x^6 +114*x^3 -1)). - Colin Barker, Nov 28 2013
a(n) = 12998*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Jan 12 2014
MATHEMATICA
Denominator[Convergents[Sqrt[520], 40]] (* Vincenzo Librandi, Jan 12 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 12998, 0, 0, 0, 0, 0, -1}, {1, 1, 5, 56, 229, 285, 12769, 13054, 64985, 727889, 2976541, 3704430}, 30] (* Harvey P. Dale, Jan 30 2023 *)
PROG
(Magma) I:=[1, 1, 5, 56, 229, 285, 12769, 13054, 64985, 727889, 2976541, 3704430]; [n le 12 select I[n] else 12998*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Jan 12 2014
CROSSREFS
Sequence in context: A289259 A072318 A174514 * A288543 A062125 A030060
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 28 2013
STATUS
approved