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A041891
Denominators of continued fraction convergents to sqrt(467).
2
1, 1, 2, 3, 5, 18, 59, 1257, 3830, 12747, 16577, 29324, 45901, 75225, 3205351, 3280576, 6485927, 9766503, 16252430, 58523793, 191823809, 4086823782, 12452295155, 41443709247, 53896004402, 95339713649, 149235718051, 244575431700, 10421403849451, 10665979281151
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, 3251252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^26 -x^25 +2*x^24 -3*x^23 +5*x^22 -18*x^21 +59*x^20 -1257*x^19 +3830*x^18 -12747*x^17 +16577*x^16 -29324*x^15 +45901*x^14 -75225*x^13 -45901*x^12 -29324*x^11 -16577*x^10 -12747*x^9 -3830*x^8 -1257*x^7 -59*x^6 -18*x^5 -5*x^4 -3*x^3 -2*x^2 -x -1)/(x^28 -3251252*x^14 +1). - Vincenzo Librandi, Dec 26 2013
a(n) = 3251252*a(n-14) - a(n-28) for n>27. - Vincenzo Librandi, Dec 26 2013
MATHEMATICA
Denominator[Convergents[Sqrt[467], 30]] (* Harvey P. Dale, Nov 01 2011 *)
CoefficientList[Series[-(x^26 - x^25 + 2 x^24 - 3 x^23 + 5 x^22 - 18 x^21 + 59 x^20 - 1257 x^19 + 3830 x^18 - 12747 x^17 + 16577 x^16 - 29324 x^15 + 45901 x^14 - 75225 x^13 - 45901 x^12 - 29324 x^11 - 16577 x^10 - 12747 x^9 - 3830 x^8 - 1257 x^7 - 59 x^6 - 18 x^5 - 5 x^4 - 3 x^3 - 2 x^2 - x - 1)/(x^28 - 3251252 x^14 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 26 2013 *)
PROG
(Magma) I:=[1, 1, 2, 3, 5, 18, 59, 1257, 3830, 12747, 16577, 29324, 45901, 75225, 3205351, 3280576, 6485927, 9766503, 16252430, 58523793, 191823809, 4086823782, 12452295155, 41443709247, 53896004402, 95339713649, 149235718051, 244575431700]; [n le 28 select I[n] else 3251252*Self(n-14)-Self(n-28): n in [1..50]]; // Vincenzo Librandi, Dec 26 2013
CROSSREFS
Cf. A041890.
Sequence in context: A041293 A041713 A042555 * A042813 A128532 A130076
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Dec 26 2013
STATUS
approved