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A041893
Denominators of continued fraction convergents to sqrt(468).
2
1, 1, 2, 3, 8, 11, 19, 30, 1279, 1309, 2588, 3897, 10382, 14279, 24661, 38940, 1660141, 1699081, 3359222, 5058303, 13475828, 18534131, 32009959, 50544090, 2154861739, 2205405829, 4360267568, 6565673397, 17491614362, 24057287759, 41548902121, 65606189880
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1298,0,0,0,0,0,0,0,-1).
FORMULA
G.f.: -(x^2-x-1)*(x^4+3*x^2+1)*(x^8+10*x^4+1) / ((x^8-36*x^4-1)*(x^8+36*x^4-1)). - Colin Barker, Nov 26 2013
a(n) = 1298*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 26 2013
MATHEMATICA
Denominator[Convergents[Sqrt[468], 50]] (* Harvey P. Dale, Sep 19 2011 *)
CoefficientList[Series[-(x^14 - x^13 + 2 x^12 - 3 x^11 + 8 x^10 - 11 x^9 + 19 x^8 - 30 x^7 - 19 x^6 - 11 x^5 - 8 x^4 - 3 x^3 - 2 x^2 - x - 1)/(x^16 - 1298 x^8 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 26 2013 *)
PROG
(Magma) I:=[1, 1, 2, 3, 8, 11, 19, 30, 1279, 1309, 2588, 3897, 10382, 14279, 24661, 38940]; [n le 16 select I[n] else 1298*Self(n-8)-Self(n-16): n in [1..50]]; // Vincenzo Librandi, Dec 26 2013
CROSSREFS
Sequence in context: A091076 A112595 A041075 * A206241 A295333 A113873
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 26 2013
STATUS
approved