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A041643
Denominators of continued fraction convergents to sqrt(340).
2
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
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
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Dec 22 2013
STATUS
approved