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A042324
Numerators of continued fraction convergents to sqrt(689).
2
26, 105, 5486, 22049, 1152034, 4630185, 241921654, 972316801, 50802395306, 204181898025, 10668261092606, 42877226268449, 2240284027051954, 9004013334476265, 470448977419817734, 1890799923013747201
OFFSET
0,1
FORMULA
G.f.: (26 +105*x +26*x^2 -x^3)/(1 -210*x^2 +x^4). - Vincenzo Librandi Nov 21 2013
a(n) = 210*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 21 2013
MATHEMATICA
Numerator[Convergents[Sqrt[689], 30]] (* or *) CoefficientList[Series[(26 + 105 x + 26 x^2 - x^3)/(1 -210 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 21 2013 *)
LinearRecurrence[{0, 210, 0, -1}, {26, 105, 5486, 22049}, 20] (* Harvey P. Dale, May 12 2017 *)
PROG
(Magma) I:=[26, 105, 5486, 22049]; [n le 4 select I[n] else 210*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013
CROSSREFS
Cf. A042325.
Sequence in context: A244633 A042320 A042322 * A044277 A044658 A024381
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved