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A041857 Denominators of continued fraction convergents to sqrt(450). 2
1, 4, 5, 14, 61, 136, 197, 924, 39005, 156944, 195949, 548842, 2391317, 5331476, 7722793, 36222648, 1529074009, 6152518684, 7681592693, 21515704070, 93744408973, 209004522016, 302748930989, 1420000245972, 59942759261813, 241191037293224 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,39202,0,0,0,0,0,0,0,-1).
FORMULA
G.f.: -(x^14 -4*x^13 +5*x^12 -14*x^11 +61*x^10 -136*x^9 +197*x^8 -924*x^7 -197*x^6 -136*x^5 -61*x^4 -14*x^3 -5*x^2 -4*x -1) / ((x^4 -14*x^2 -1)*(x^4 +14*x^2 -1)*(x^8 +198*x^4 +1)). - Colin Barker, Nov 26 2013
a(n) = 39202*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 26 2013
MATHEMATICA
Denominator[Convergents[Sqrt[450], 30] (]* Vincenzo Librandi, Dec 26 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 39202, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 4, 5, 14, 61, 136, 197, 924, 39005, 156944, 195949, 548842, 2391317, 5331476, 7722793, 36222648}, 30] (* Harvey P. Dale, Jan 26 2024 *)
PROG
(Magma) I:=[1, 4, 5, 14, 61, 136, 197, 924, 39005, 156944, 195949, 548842, 2391317, 5331476, 7722793, 36222648]; [n le 16 select I[n] else 39202*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 26 2013
CROSSREFS
Sequence in context: A042279 A352683 A182252 * A041034 A281911 A042535
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 26 2013
STATUS
approved

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Last modified July 13 12:36 EDT 2024. Contains 374284 sequences. (Running on oeis4.)