|
| |
|
|
A041453
|
|
Denominators of continued fraction convergents to sqrt(242).
|
|
2
|
|
|
|
1, 1, 2, 7, 9, 133, 142, 559, 701, 1260, 38501, 39761, 78262, 274547, 352809, 5213873, 5566682, 21913919, 27480601, 49394520, 1509316201, 1558710721, 3068026922, 10762791487, 13830818409, 204394249213, 218225067622, 859069452079, 1077294519701, 1936363971780
(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 (0,0,0,0,0,0,0,0,0,39202,0,0,0,0,0,0,0,0,0,-1).
|
|
|
FORMULA
|
G.f.: -(x^18 -x^17 +2*x^16 -7*x^15 +9*x^14 -133*x^13 +142*x^12 -559*x^11 +701*x^10 -1260*x^9 -701*x^8 -559*x^7 -142*x^6 -133*x^5 -9*x^4 -7*x^3 -2*x^2 -x -1) / ((x^10 -198*x^5 +1)*(x^10 +198*x^5 +1)). - Colin Barker, Nov 17 2013
a(n) = 39202*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 18 2013
|
|
|
MATHEMATICA
|
Denominator[Convergents[Sqrt[242], 30]] (* Vincenzo Librandi, Dec 18 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 39202, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 2, 7, 9, 133, 142, 559, 701, 1260, 38501, 39761, 78262, 274547, 352809, 5213873, 5566682, 21913919, 27480601, 49394520}, 40] (* Harvey P. Dale, May 05 2022 *)
|
|
|
PROG
|
(Magma) I:=[1, 1, 2, 7, 9, 133, 142, 559, 701, 1260, 38501, 39761, 78262, 274547, 352809, 5213873, 5566682, 21913919, 27480601, 49394520]; [n le 20 select I[n] else 39202*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 18 2013
|
|
|
CROSSREFS
|
Cf. A041452, A040226.
Sequence in context: A272412 A042561 A252661 * A042157 A012937 A022414
Adjacent sequences: A041450 A041451 A041452 * A041454 A041455 A041456
|
|
|
KEYWORD
|
nonn,frac,easy
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
EXTENSIONS
|
More terms from Colin Barker, Nov 17 2013
|
|
|
STATUS
|
approved
|
| |
|
|
