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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041251 Denominators of continued fraction convergents to sqrt(137). 2
1, 1, 3, 7, 10, 17, 44, 105, 149, 3383, 3532, 10447, 24426, 34873, 59299, 153471, 366241, 519712, 11799905, 12319617, 36439139, 85197895, 121637034, 206834929, 535306892, 1277448713, 1812755605, 41158072023, 42970827628, 127099727279, 297170282186 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,3488,0,0,0,0,0,0,0,0,1).

FORMULA

G.f.: -(x^16 -x^15 +3*x^14 -7*x^13 +10*x^12 -17*x^11 +44*x^10 -105*x^9 +149*x^8 +105*x^7 +44*x^6 +17*x^5 +10*x^4 +7*x^3 +3*x^2 +x +1) / (x^18 +3488*x^9 -1). - Colin Barker, Nov 14 2013

a(n) = 3488*a(n-9) + a(n-18). - Vincenzo Librandi, Dec 13 2013

MATHEMATICA

Denominator[Convergents[Sqrt[137], 30]]  (* Vincenzo Librandi, Dec 13 2013 *)

PROG

(MAGMA) I:=[1, 1, 3, 7, 10, 17, 44, 105, 149, 3383, 3532, 10447, 24426, 34873, 59299, 153471, 366241, 519712]; [n le 18 select I[n] else 3488*Self(n-9)+Self(n-18): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

CROSSREFS

Cf. A041250, A010196.

Sequence in context: A304216 A305247 A316547 * A042435 A042591 A098001

Adjacent sequences:  A041248 A041249 A041250 * A041252 A041253 A041254

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 14 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 December 2 17:56 EST 2021. Contains 349445 sequences. (Running on oeis4.)