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A041589
Denominators of continued fraction convergents to sqrt(312).
2
1, 1, 2, 3, 104, 107, 211, 318, 11023, 11341, 22364, 33705, 1168334, 1202039, 2370373, 3572412, 123832381, 127404793, 251237174, 378641967, 13125064052, 13503706019, 26628770071, 40132476090, 1391132957131, 1431265433221, 2822398390352, 4253663823573
OFFSET
0,3
FORMULA
G.f.: -(x^2-x-1)*(x^4+3*x^2+1) / (x^8-106*x^4+1). - Colin Barker, Nov 19 2013
a(n) = 106*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 20 2013
MATHEMATICA
Denominator/@Convergents[Sqrt[312], 30] (* Harvey P. Dale, Jun 04 2011 *)
CoefficientList[Series[(1 + x - x^2) (x^4 + 3 x^2 + 1)/(x^8 - 106 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 20 2013 *)
PROG
(Magma) I:=[1, 1, 2, 3, 104, 107, 211, 318]; [n le 8 select I[n] else 106*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013
CROSSREFS
Sequence in context: A256114 A345336 A062657 * A371122 A371229 A039768
KEYWORD
nonn,frac,easy
EXTENSIONS
More terms from Colin Barker, Nov 19 2013
STATUS
approved