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A041379
Denominators of continued fraction convergents to sqrt(204).
2
1, 3, 4, 7, 46, 53, 99, 350, 9899, 30047, 39946, 69993, 459904, 529897, 989801, 3499300, 98970201, 300409903, 399380104, 699790007, 4598120146, 5297910153, 9896030299, 34986001050, 989504059699, 3003498180147, 3993002239846, 6996500419993, 45972004759804
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,9998,0,0,0,0,0,0,0,-1).
FORMULA
G.f.: -(x^14 -3*x^13 +4*x^12 -7*x^11 +46*x^10 -53*x^9 +99*x^8 -350*x^7 -99*x^6 -53*x^5 -46*x^4 -7*x^3 -4*x^2 -3*x -1) / ((x^8 -100*x^4 +1)*(x^8 +100*x^4 +1)). - Colin Barker, Nov 16 2013
a(n) = 9998*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 16 2013
MATHEMATICA
Denominator[Convergents[Sqrt[204], 30]] (* Vincenzo Librandi, Dec 16 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 9998, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 3, 4, 7, 46, 53, 99, 350, 9899, 30047, 39946, 69993, 459904, 529897, 989801, 3499300}, 30] (* Harvey P. Dale, Jul 22 2021 *)
PROG
(Magma) I:=[1, 3, 4, 7, 46, 53, 99, 350, 9899, 30047, 39946, 69993, 459904, 529897, 989801, 3499300]; [n le 16 select I[n] else 9998*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013
CROSSREFS
Sequence in context: A084590 A279920 A041135 * A242859 A134471 A256725
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 16 2013
STATUS
approved