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A041905
Denominators of continued fraction convergents to sqrt(474).
2
1, 1, 4, 9, 13, 22, 35, 232, 267, 499, 766, 2031, 6859, 8890, 380239, 389129, 1547626, 3484381, 5032007, 8516388, 13548395, 89806758, 103355153, 193161911, 296517064, 786196039, 2655105181, 3441301220, 147189756421, 150631057641, 599082929344
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, 387098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^26 -x^25 +4*x^24 -9*x^23 +13*x^22 -22*x^21 +35*x^20 -232*x^19 +267*x^18 -499*x^17 +766*x^16 -2031*x^15 +6859*x^14 -8890*x^13 -6859*x^12 -2031*x^11 -766*x^10 -499*x^9 -267*x^8 -232*x^7 -35*x^6 -22*x^5 -13*x^4 -9*x^3 -4*x^2 -x -1)/(x^28 -387098*x^14 +1). - Vincenzo Librandi, Dec 26 2013
a(n) = 387098*a(n-14) - a(n-28) for n>27. - Vincenzo Librandi, Dec 26 2013
MATHEMATICA
Denominator[Convergents[Sqrt[474], 30]] (* or *) CoefficientList[Series[-(x^26 - x^25 + 4 * x^24 - 9 * x^23 + 13 * x^22 - 22 * x^21 + 35 * x^20 - 232 * x^19 + 267 * x^18 - 499 * x^17 + 766 * x^16 - 2031 * x^15 + 6859 * x^14 - 8890 * x^13 - 6859 * x^12 - 2031 * x^11 - 766 * x^10 - 499 * x^9 - 267 * x^8 - 232 * x^7 - 35 * x^6 - 22 * x^5 - 13 * x^4 - 9 * x^3 - 4 * x^2 - x - 1)/(x^28 - 387098 * x^14 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 26 2013 *)
PROG
(Magma) I:=[1, 1, 4, 9, 13, 22, 35, 232, 267, 499, 766, 2031, 6859, 8890, 380239, 389129, 1547626, 3484381, 5032007, 8516388, 13548395, 89806758, 103355153, 193161911, 296517064, 786196039, 2655105181, 3441301220]; [n le 28 select I[n] else 387098*Self(n-14)-Self(n-28): n in [1..50]]; // Vincenzo Librandi, Dec 26 2013
CROSSREFS
Cf. A041904.
Sequence in context: A345743 A022130 A042125 * A098004 A257337 A056227
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Dec 26 2013
STATUS
approved