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A042075 Denominators of continued fraction convergents to sqrt(561). 2
1, 1, 3, 16, 19, 35, 89, 213, 515, 728, 1243, 6943, 15129, 22072, 1030441, 1052513, 3135467, 16729848, 19865315, 36595163, 93055641, 222706445, 538468531, 761174976, 1299643507, 7259392511, 15818428529, 23077821040, 1077398196369, 1100476017409 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1045570, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^26 -x^25 +3*x^24 -16*x^23 +19*x^22 -35*x^21 +89*x^20 -213*x^19 +515*x^18 -728*x^17 +1243*x^16 -6943*x^15 +15129*x^14 -22072*x^13 -15129*x^12 -6943*x^11 -1243*x^10 -728*x^9 -515*x^8 -213*x^7 -89*x^6 -35*x^5 -19*x^4 -16*x^3 -3*x^2 -x -1)/(x^28 -1045570*x^14 +1). - Vincenzo Librandi, Jan 14 2014
a(n) = 1045570*a(n-14) - a(n-28)for n>27. - Vincenzo Librandi, Jan 14 2014
MATHEMATICA
Denominator[Convergents[Sqrt[561], 30]] (* or *) CoefficientList[Series[-(x^26 - x^25 + 3 x^24 - 16 x^23 + 19 x^22 - 35 x^21 + 89 x^20 - 213 x^19 + 515 x^18 - 728 x^17 + 1243 x^16 - 6943 x^15 + 15129 x^14 - 22072 x^13 - 15129 x^12 - 6943 x^11 - 1243 x^10 - 728 x^9 - 515 x^8 - 213 x^7 - 89 x^6 - 35 x^5 - 19 x^4 - 16 x^3 - 3 x^2 - x - 1)/(x^28 - 1045570 x^14 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Jan 14 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1045570, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 3, 16, 19, 35, 89, 213, 515, 728, 1243, 6943, 15129, 22072, 1030441, 1052513, 3135467, 16729848, 19865315, 36595163, 93055641, 222706445, 538468531, 761174976, 1299643507, 7259392511, 15818428529, 23077821040}, 30] (* Harvey P. Dale, Mar 01 2015 *)
CROSSREFS
Cf. A042074.
Sequence in context: A103655 A022126 A127006 * A342716 A042777 A041461
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Jan 14 2014
STATUS
approved

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Last modified March 28 07:48 EDT 2024. Contains 371235 sequences. (Running on oeis4.)