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URL: https://oeis.org/A041188

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A041188
Numerators of continued fraction convergents to sqrt(105).
2
10, 41, 830, 3361, 68050, 275561, 5579270, 22592641, 457432090, 1852321001, 37503852110, 151867729441, 3074858440930, 12451301493161, 252100888304150, 1020854854709761, 20669197982499370, 83697646784707241
OFFSET
0,1
LINKS
Vincenzo Librandi and Bruno Berselli, Table of n, a(n) for n = 0..100 (first 91 terms from Vincenzo Librandi).
FORMULA
G.f.: (10 + 41*x + 10*x^2 - x^3) / (1 - 82*x^2 + x^4). [Bruno Berselli, Oct 30 2013]
a(n) = 82*a(n-2) - a(n-4). [Bruno Berselli, Oct 30 2013]
MATHEMATICA
Numerator[Convergents[Sqrt[105], 30]] (* Vincenzo Librandi, Oct 30 2013 *)
RecurrenceTable[{a[0] == 10, a[1] == 41, a[2] == 830, a[3] == 3361, a[n] == 82 a[n - 2] - a[n - 4]}, a, {n, 0, 20}] (* Bruno Berselli, Oct 30 2013 *)
CROSSREFS
Cf. A041189.
Sequence in context: A089211 A220927 A222858 * A113683 A385409 A330790
KEYWORD
nonn,cofr,frac,easy
STATUS
approved