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A041435 Denominators of continued fraction convergents to sqrt(233). 2
1, 3, 4, 15, 19, 34, 53, 87, 314, 401, 1517, 45911, 139250, 185161, 694733, 879894, 1574627, 2454521, 4029148, 14541965, 18571113, 70255304, 2126230233, 6448946003, 8575176236, 32174474711, 40749650947, 72924125658, 113673776605, 186597902263, 673467483394 (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, 0, 0, 0, 46312, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
FORMULA
G.f.: -(x^20 -3*x^19 +4*x^18 -15*x^17 +19*x^16 -34*x^15 +53*x^14 -87*x^13 +314*x^12 -401*x^11 +1517*x^10 +401*x^9 +314*x^8 +87*x^7 +53*x^6 +34*x^5 +19*x^4 +15*x^3 +4*x^2 +3*x +1) / (x^22 +46312*x^11 -1). - Colin Barker, Nov 17 2013
a(n) = 46312*a(n-11) + a(n-22) for n>21. - Vincenzo Librandi, Dec 17 2013
MATHEMATICA
Denominator[Convergents[Sqrt[233], 30]] (* Vincenzo Librandi, Dec 17 2013 *)
PROG
(Magma) I:=[1, 3, 4, 15, 19, 34, 53, 87, 314, 401, 1517, 45911, 139250, 185161, 694733, 879894, 1574627, 2454521, 4029148, 14541965, 18571113, 70255304]; [n le 22 select I[n] else 46312*Self(n-11)+Self(n-22): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013
CROSSREFS
Sequence in context: A053359 A056742 A338123 * A136210 A041819 A369910
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 17 2013
STATUS
approved

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Last modified June 12 15:44 EDT 2024. Contains 373332 sequences. (Running on oeis4.)