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!)
A042902 Numerators of continued fraction convergents to sqrt(983). 2
31, 63, 94, 533, 16617, 83618, 100235, 284088, 17713691, 35711470, 53425161, 302837275, 9441380686, 47509740705, 56951121391, 161411983487, 10064494097585, 20290400178657, 30354894276242, 172064871559867, 5364365912632119, 26993894434720462, 32358260347352581 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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, 568176, 0, 0, 0, 0, 0, 0, 0, -1).

FORMULA

G.f.: (31 +63*x +94*x^2 +533*x^3 +16617*x^4 +83618*x^5 +100235*x^6 +284088*x^7 +100235*x^8 -83618*x^9 +16617*x^10 -533*x^11 +94*x^12 -63*x^13 +31*x^14 -x^15)/(1 -568176*x^8 +x^16). - Vincenzo Librandi, Dec 09 2013

a(n) = 568176*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 09 2013

MATHEMATICA

Numerator[Convergents[Sqrt[983], 30]] (* or *) CoefficientList[Series[(31 + 63 x + 94 x^2 + 533 x^3 + 16617 x^4 + 83618 x^5 + 100235 x^6 + 284088 x^7 + 100235 x^8 - 83618 x^9 + 16617 x^10 - 533 x^11 + 94 x^12 - 63 x^13 + 31 x^14 - x^15)/(1 - 568176 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2013 *)

PROG

(MAGMA) I:=[31, 63, 94, 533, 16617, 83618, 100235, 284088, 17713691, 35711470, 53425161, 302837275, 9441380686, 47509740705, 56951121391, 161411983487]; [n le 16 select I[n] else 568176*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Dec 09 2013

CROSSREFS

Cf. A042903.

Sequence in context: A276787 A042906 A042904 * A042900 A239128 A042910

Adjacent sequences:  A042899 A042900 A042901 * A042903 A042904 A042905

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Dec 09 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 April 19 17:46 EDT 2021. Contains 343117 sequences. (Running on oeis4.)