A041403 Denominators of continued fraction convergents to sqrt(216).
1, 1, 3, 10, 23, 33, 947, 980, 2907, 9701, 22309, 32010, 918589, 950599, 2819787, 9409960, 21639707, 31049667, 891030383, 922080050, 2735190483, 9127651499, 20990493481, 30118144980, 864298552921, 894416697901, 2653131948723, 8853812544070, 20360757036863
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,970,0,0,0,0,0,-1).
Programs
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Magma
I:=[1,1,3,10,23,33,947,980,2907,9701,22309, 32010]; [n le 12 select I[n] else 970*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013
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Mathematica
Denominator[Convergents[Sqrt[216], 30]] (* Vincenzo Librandi, Dec 17 2013 *)
Formula
G.f.: -(x^10 -x^9 +3*x^8 -10*x^7 +23*x^6 -33*x^5 -23*x^4 -10*x^3 -3*x^2 -x -1) / ((x^4 -10*x^2 +1)*(x^8 +10*x^6 +99*x^4 +10*x^2 +1)). - Colin Barker, Nov 17 2013
a(n) = 970*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 17 2013
Extensions
More terms from Colin Barker, Nov 17 2013