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A041205 Denominators of continued fraction convergents to sqrt(113). 2
1, 1, 2, 3, 8, 19, 27, 46, 73, 1506, 1579, 3085, 4664, 12413, 29490, 41903, 71393, 113296, 2337313, 2450609, 4787922, 7238531, 19264984, 45768499, 65033483, 110801982, 175835465, 3627511282, 3803346747, 7430858029, 11234204776, 29899267581, 71032739938 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1552,0,0,0,0,0,0,0,0,1).
FORMULA
G.f.: -(x^16 -x^15 +2*x^14 -3*x^13 +8*x^12 -19*x^11 +27*x^10 -46*x^9 +73*x^8 +46*x^7 +27*x^6 +19*x^5 +8*x^4 +3*x^3 +2*x^2 +x +1) / (x^18 +1552*x^9 -1). - Colin Barker, Nov 14 2013
a(n) = 1552*a(n-9) + a(n-18). - Vincenzo Librandi, Dec 13 2013
MATHEMATICA
Denominator[Convergents[Sqrt[113], 40]] (* Harvey P. Dale, Feb 05 2012 *)
CoefficientList[Series[-(x^16 - x^15 + 2 x^14 - 3 x^13 + 8 x^12 - 19 x^11 + 27 x^10 - 46 x^9 + 73 x^8 + 46 x^7 + 27 x^6 + 19 x^5 + 8 x^4 + 3 x^3 + 2 x^2 + x + 1)/(x^18 + 1552 x^9 - 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 13 2013 *)
PROG
(Magma) I:=[1, 1, 2, 3, 8, 19, 27, 46, 73, 1506, 1579, 3085, 4664, 12413, 29490, 41903, 71393, 113296]; [n le 18 select I[n] else 1552*Self(n-9)+Self(n-18): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013
CROSSREFS
Sequence in context: A240645 A273754 A242099 * A002356 A166302 A347736
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 14 2013
STATUS
approved

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Last modified March 29 17:57 EDT 2024. Contains 371280 sequences. (Running on oeis4.)