|
| |
|
|
A041597
|
|
Denominators of continued fraction convergents to sqrt(316).
|
|
2
|
|
|
|
1, 1, 4, 9, 76, 161, 559, 720, 25039, 25759, 102316, 230391, 1945444, 4121279, 14309281, 18430560, 640948321, 659378881, 2619084964, 5897548809, 49799475436, 105496499681, 366288974479, 471785474160, 16406995095919, 16878780570079, 67043336806156
(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 (0,0,0,0,0,0,0,25598,0,0,0,0,0,0,0,-1).
|
|
|
FORMULA
|
G.f.: -(x^14 -x^13 +4*x^12 -9*x^11 +76*x^10 -161*x^9 +559*x^8 -720*x^7 -559*x^6 -161*x^5 -76*x^4 -9*x^3 -4*x^2 -x -1) / ((x^8 -160*x^4 +1)*(x^8 +160*x^4 +1)). - Colin Barker, Nov 19 2013
a(n) = 25598*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 21 2013
|
|
|
MATHEMATICA
|
Denominator[Convergents[Sqrt[316], 30]] (* Vincenzo Librandi Dec 21 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 25598, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 4, 9, 76, 161, 559, 720, 25039, 25759, 102316, 230391, 1945444, 4121279, 14309281, 18430560}, 30] (* Harvey P. Dale, Mar 21 2017 *)
|
|
|
PROG
|
(MAGMA) I:=[1, 1, 4, 9, 76, 161, 559, 720, 25039, 25759, 102316, 230391, 1945444, 4121279, 14309281, 18430560]; [n le 16 select I[n] else 25598*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 21 2013
|
|
|
CROSSREFS
|
Cf. A041596, A040298.
Sequence in context: A122956 A041777 A100517 * A041030 A061104 A082381
Adjacent sequences: A041594 A041595 A041596 * A041598 A041599 A041600
|
|
|
KEYWORD
|
nonn,frac,easy
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
EXTENSIONS
|
More terms from Colin Barker, Nov 19 2013
|
|
|
STATUS
|
approved
|
| |
|
|
