A041283 Denominators of continued fraction convergents to sqrt(154).

1, 2, 5, 17, 22, 61, 83, 310, 703, 1716, 41887, 85490, 212867, 724091, 936958, 2598007, 3534965, 13202902, 29940769, 73084440, 1783967329, 3641019098, 9066005525, 30839035673, 39905041198, 110649118069, 150554159267, 562311595870, 1275177351007

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,42590,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -2*x^17 +5*x^16 -17*x^15 +22*x^14 -61*x^13 +83*x^12 -310*x^11 +703*x^10 -1716*x^9 -703*x^8 -310*x^7 -83*x^6 -61*x^5 -22*x^4 -17*x^3 -5*x^2 -2*x -1) / (x^20 -42590*x^10 +1). - Colin Barker, Nov 14 2013

a(n) = 42590*af(n-10) - a(n-20). - Vincenzo Librandi, Dec 14 2013

Mathematica

Denominator/@Convergents[Sqrt[154], 30] (* Harvey P. Dale, Jul 13 2011 *)
CoefficientList[Series[-(x^18 - 2 x^17 + 5 x^16 - 17 x^15 + 22 x^14 - 61 x^13 + 83 x^12 - 310 x^11 + 703 x^10 - 1716 x^9 - 703 x^8 - 310 x^7 - 83 x^6 - 61 x^5 - 22 x^4 - 17 x^3 - 5 x^2 - 2 x - 1)/(x^20 - 42590 x^10 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 14 2013 *)

Prog

(Magma) I:=[1, 2, 5, 17, 22, 61, 83, 310, 703, 1716, 41887, 85490, 212867, 724091, 936958, 2598007, 3534965, 13202902, 29940769, 73084440]; [n le 20 select I[n] else 42590*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 14 2013

Crossrefs

Cf. A041282, A010205.

Sequence in context: A075612 A156010 A215273 * A042049 A341017 A069689

Adjacent sequences: A041280 A041281 A041282 * A041284 A041285 A041286

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved