login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041447 Denominators of continued fraction convergents to sqrt(239). 2
1, 2, 11, 13, 37, 161, 2452, 9969, 22390, 32359, 184185, 400729, 12206055, 24812839, 136270250, 161083089, 458436428, 1994828801, 30380868443, 123518302573, 277417473589, 400935776162, 2282096354399, 4965128484960, 151235950903199, 307437030291358 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,12390240,0,0,0,0,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: (1 +2*x +11*x^2 +13*x^3 +37*x^4 +161*x^5 +2452*x^6 +9969*x^7 +22390*x^8 +32359*x^9 +184185*x^10 +400729*x^11 -184185*x^12 +32359*x^13 -22390*x^14 +9969*x^15 -2452*x^16 +161*x^17 -37*x^18 +13*x^19 -11*x^20 +2*x^21 -x^22)/(1 -12390240*x^12 +x^24). - Vincenzo Librandi, Dec 18 2013

a(n) = 12390240*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 18 2013

MATHEMATICA

Denominator[Convergents[Sqrt[239], 30]] (* or *) CoefficientList[Series[(1 +2 x + 11 x^2 + 13 x^3 + 37 x^4 + 161 x^5 + 2452 x^6 + 9969 x^7 + 22390 x^8 + 32359 x^9 + 184185 x^10 + 400729 x^11 - 184185 x^12 + 32359 x^13 - 22390 x^14 + 9969 x^15 - 2452 x^16 + 161 x^17 - 37 x^18 + 13 x^19 - 11 x^20 + 2 x^21 - x^22)/(1 - 12390240 x^12 + x^24), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 18 2013 *)

PROG

(MAGMA) I:=[1, 2, 11, 13, 37, 161, 2452, 9969, 22390, 32359, 184185, 400729, 12206055, 24812839, 136270250, 161083089, 458436428, 1994828801, 30380868443, 123518302573, 277417473589, 400935776162, 2282096354399, 4965128484960]; [n le 24 select I[n] else 12390240*Self(n-12)-Self(n-24): n in [1..30]]; // Vincenzo Librandi, Dec 18 2013

CROSSREFS

Cf. A041446.

Sequence in context: A023288 A106960 A084405 * A291464 A262832 A091021

Adjacent sequences:  A041444 A041445 A041446 * A041448 A041449 A041450

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Dec 18 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 22 18:05 EST 2019. Contains 320400 sequences. (Running on oeis4.)