A041643 Denominators of continued fraction convergents to sqrt(340).

1, 2, 7, 9, 16, 25, 41, 353, 394, 747, 1141, 1888, 6805, 15498, 564733, 1144964, 3999625, 5144589, 9144214, 14288803, 23433017, 201752939, 225185956, 426938895, 652124851, 1079063746, 3889316089, 8857695924, 322766369353, 654390434630

Offset

0,2

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, 571538, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^26 -2*x^25 +7*x^24 -9*x^23 +16*x^22 -25*x^21 +41*x^20 -353*x^19 +394*x^18 -747*x^17 +1141*x^16 -1888*x^15 +6805*x^14 -15498*x^13 -6805*x^12 -1888*x^11 -1141*x^10 -747*x^9 -394*x^8 -353*x^7 -41*x^6 -25*x^5 -16*x^4 -9*x^3 -7*x^2 -2*x -1)/(x^28 -571538*x^14 +1). - Vincenzo Librandi, Dec 22 2013

a(n) = 571538*a(n-14) - a(n-28) for n>27. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[340], 30]] (* Harvey P. Dale, Jun 01 2012 *)
CoefficientList[Series[-(x^26 - 2 x^25 + 7 x^24 - 9 x^23 + 16 x^22 - 25 x^21 + 41 x^20 - 353 x^19 + 394 x^18 - 747 x^17 + 1141 x^16 - 1888 x^15 + 6805 x^14 - 15498 x^13 - 6805 x^12 - 1888 x^11 - 1141 x^10 - 747 x^9 - 394 x^8 - 353 x^7 - 41 x^6 - 25 x^5 - 16 x^4 - 9 x^3 - 7 x^2 - 2 x - 1)/(x^28 - 571538 x^14 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 22 2013 *)

Prog

(Magma) I:=[1, 2, 7, 9, 16, 25, 41, 353, 394, 747, 1141, 1888, 6805, 15498, 564733, 1144964, 3999625, 5144589, 9144214, 14288803, 23433017, 201752939, 225185956, 426938895, 652124851, 1079063746, 3889316089, 8857695924]; [n le 28 select I[n] else 571538*Self(n-14)-Self(n-28): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041642.

Sequence in context: A287575 A267212 A022113 * A041395 A042345 A041973

Adjacent sequences: A041640 A041641 A041642 * A041644 A041645 A041646

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 22 2013

Status

approved