A041537 Denominators of continued fraction convergents to sqrt(285).
1, 1, 8, 17, 127, 144, 4735, 4879, 38888, 82655, 617473, 700128, 23021569, 23721697, 189073448, 401868593, 3002153599, 3404022192, 111930863743, 115334885935, 919275065288, 1953885016511, 14596470180865, 16550355197376, 544207836496897, 560758191694273
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, 4862, 0, 0, 0, 0, 0, -1).
Programs
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Magma
I:=[1,1,8,17,127,144,4735,4879,38888,82655, 617473,700128]; [n le 12 select I[n] else 4862*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 19 2013
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Mathematica
Denominator[Convergents[Sqrt[285], 30]] (* Harvey P. Dale, Nov 08 2013 *) CoefficientList[Series[-(x^10 - x^9 + 8 x^8 - 17 x^7 + 127 x^6 - 144 x^5 - 127 x^4 - 17 x^3 - 8 x^2 - x - 1)/((x^4 - 17 x^2 + 1) (x^8 + 17 x^6 + 288 x^4 + 17 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 19 2013 *)
Formula
G.f.: -(x^10 -x^9 +8*x^8 -17*x^7 +127*x^6 -144*x^5 -127*x^4 -17*x^3 -8*x^2 -x -1) / ((x^4 -17*x^2 +1)*(x^8 +17*x^6 +288*x^4 +17*x^2 +1)). - Colin Barker, Nov 18 2013
a(n) = 4862*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 19 2013
Extensions
More terms from Colin Barker, Nov 18 2013