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A041657
Denominators of continued fraction convergents to sqrt(347).
2
1, 1, 2, 3, 8, 35, 43, 766, 809, 4002, 8813, 12815, 21628, 34443, 1261576, 1296019, 2557595, 3853614, 10264823, 44912906, 55177729, 982934299, 1038112028, 5135382411, 11308876850, 16444259261, 27753136111, 44197395372, 1618859369503, 1663056764875
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, 1283204, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: (1 +x +2*x^2 +3*x^3 +8*x^4 +35*x^5 +43*x^6 +766*x^7 +809*x^8 +4002*x^9 +8813*x^10 +12815*x^11 +21628*x^12 +34443*x^13 -21628*x^14 +12815*x^15 -8813*x^16 +4002*x^17 -809*x^18 +766*x^19 -43*x^20 +35*x^21 -8*x^22 +3*x^23 -2*x^24 +x^25 -x^26)/(1 -1283204*x^14 +x^28). - Vincenzo Librandi, Dec 22 2013
a(n) = 1283204*a(n-14) - a(n-28) for n>27. - Vincenzo Librandi, Dec 22 2013
MATHEMATICA
Denominator[Convergents[Sqrt[347], 30]] (* or *) CoefficientList[Series[(1 + x + 2 x^2 + 3 x^3 + 8 x^4 + 35 x^5 + 43 x^6 + 766 x^7 + 809 x^8 + 4002 x^9 + 8813 x^10 + 12815 x^11 + 21628 x^12 + 34443 x^13 - 21628 x^14 + 12815 x^15 - 8813 x^16 + 4002 x^17 - 809 x^18 + 766 x^19 - 43 x^20 + 35 x^21 - 8 x^22 + 3 x^23 - 2 x^24 + x^25 - x^26)/(1 - 1283204 x^14 + x^28), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 22 2013 *)
CROSSREFS
Cf. A041656.
Sequence in context: A078742 A005370 A112866 * A191274 A041789 A174899
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Dec 22 2013
STATUS
approved