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A041768
Numerators of continued fraction convergents to sqrt(405).
2
20, 161, 6460, 51841, 2080100, 16692641, 669785740, 5374978561, 215668928180, 1730726404001, 69444725088220, 557288527109761, 22360985809478660, 179445175002939041, 7200167985927040300, 57780789062419261441, 2318431730482697497940, 18605234632923999244961
OFFSET
0,1
FORMULA
G.f.: -(x^3-20*x^2-161*x-20) / ((x^2-18*x+1)*(x^2+18*x+1)). - Vincenzo Librandi, Nov 08 2013, simplified by Colin Barker, Dec 28 2013
a(n) = 322*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 08 2013, simplified by Colin Barker, Dec 28 2013
MATHEMATICA
Numerator[Convergents[Sqrt[405], 30]] (* Vincenzo Librandi, Nov 07 2013 *)
CoefficientList[Series[(20 + 161 x + 6460 x^2 + 51841 x^3 + 6460 x^4 - 161 x^5 + 20 x^6 - x^7)/(1 - 103682 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 08 2013 *)
LinearRecurrence[{0, 322, 0, -1}, {20, 161, 6460, 51841}, 20] (* Harvey P. Dale, Apr 28 2022 *)
PROG
(Magma) I:=[20, 161, 6460, 51841, 2080100, 16692641, 669785740, 5374978561]; [n le 8 select I[n] else 103682*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 08 2013
CROSSREFS
Sequence in context: A126515 A118676 A067534 * A221870 A289181 A056114
KEYWORD
nonn,frac,easy,less
AUTHOR
EXTENSIONS
More terms from Colin Barker, Dec 28 2013
STATUS
approved