A041657 Denominators of continued fraction convergents to sqrt(347).

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

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, 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

Adjacent sequences: A041654 A041655 A041656 * A041658 A041659 A041660

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 22 2013

Status

approved