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A041226
Numerators of continued fraction convergents to sqrt(125).
10
11, 56, 67, 123, 682, 15127, 76317, 91444, 167761, 930249, 20633239, 104096444, 124729683, 228826127, 1268860318, 28143753123, 141987625933, 170131379056, 312119004989, 1730726404001, 38388099893011, 193671225869056, 232059325762067, 425730551631123
OFFSET
0,1
COMMENTS
From Johannes W. Meijer, Jun 12 2010: (Start)
The a(n) terms of this sequence can be constructed with the terms of sequence A001946.
For the terms of the periodical sequence of the continued fraction for sqrt(125) see A010186. We observe that its period is five. (End)
LINKS
FORMULA
From Johannes W. Meijer, Jun 12 2010: (Start)
a(5n) = A001946(3n+1),
a(5n+1) = (A001946(3n+2) - A001946(3n+1))/2,
a(5n+2) = (A001946(3n+2) + A001946(3n+1))/2,
a(5n+3) = A001946(3n+2),
a(5n+4) = A001946(3n+3)/2. (End)
G.f.: -(x^9 -11*x^8 +56*x^7 -67*x^6 +123*x^5 +682*x^4 +123*x^3 +67*x^2 +56*x +11) / ((x^2 +4*x -1)*(x^4 -7*x^3 +19*x^2 -3*x +1)*(x^4 +3*x^3 +19*x^2 +7*x +1)). - Colin Barker, Nov 08 2013
MATHEMATICA
Numerator[Convergents[Sqrt[125], 30]] (* Vincenzo Librandi, Oct 31 2013 *)
LinearRecurrence[{0, 0, 0, 0, 1364, 0, 0, 0, 0, 1}, {11, 56, 67, 123, 682, 15127, 76317, 91444, 167761, 930249}, 30] (* Harvey P. Dale, Jan 30 2026 *)
KEYWORD
nonn,cofr,frac,easy
EXTENSIONS
More terms from Colin Barker, Nov 08 2013
STATUS
approved