login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041949 Denominators of continued fraction convergents to sqrt(497). 2
1, 3, 7, 17, 92, 569, 2937, 6443, 15823, 53912, 2387951, 7217765, 16823481, 40864727, 221147116, 1367747423, 7059884231, 15487515885, 38034916001, 129592263888, 5740094527073, 17349875845107, 40439846217287, 98229568279681, 531587687615692 (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, 2403774, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

FORMULA

G.f.: -(x^18 -3*x^17 +7*x^16 -17*x^15 +92*x^14 -569*x^13 +2937*x^12 -6443*x^11 +15823*x^10 -53912*x^9 -15823*x^8 -6443*x^7 -2937*x^6 -569*x^5 -92*x^4 -17*x^3 -7*x^2 -3*x -1) / (x^20 -2403774*x^10 +1). - Colin Barker, Nov 27 2013

a(n) = 2403774*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 27 2013

MATHEMATICA

Denominator[Convergents[Sqrt[497], 30]] (* Vincenzo Librandi, Dec 27 2013 *)

PROG

(MAGMA) I:=[1, 3, 7, 17, 92, 569, 2937, 6443, 15823, 53912, 2387951, 7217765, 16823481, 40864727, 221147116, 1367747423, 7059884231, 15487515885, 38034916001, 129592263888]; [n le 20 select I[n] else 2403774*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 27 2013

CROSSREFS

Cf. A041948, A040474.

Sequence in context: A246764 A128343 A106877 * A222452 A218165 A102329

Adjacent sequences:  A041946 A041947 A041948 * A041950 A041951 A041952

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 27 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 August 14 13:10 EDT 2020. Contains 336480 sequences. (Running on oeis4.)