A041791 Denominators of continued fraction convergents to sqrt(416).

1, 2, 3, 5, 48, 53, 101, 255, 10301, 20857, 31158, 52015, 499293, 551308, 1050601, 2652510, 107151001, 216954512, 324105513, 541060025, 5193645738, 5734705763, 10928351501, 27591408765, 1114584702101, 2256760812967, 3371345515068, 5628106328035

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,10402,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -2*x^13 +3*x^12 -5*x^11 +48*x^10 -53*x^9 +101*x^8 -255*x^7 -101*x^6 -53*x^5 -48*x^4 -5*x^3 -3*x^2 -2*x -1) / ((x^4 -10*x^2 -1)*(x^4 +10*x^2 -1)*(x^8 +102*x^4 +1)). - Colin Barker, Nov 24 2013

a(n) = 10402*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 24 2013

Mathematica

Denominator[Convergents[Sqrt[416], 30]] (* Vincenzo Librandi, Dec 24 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 10402, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 2, 3, 5, 48, 53, 101, 255, 10301, 20857, 31158, 52015, 499293, 551308, 1050601, 2652510}, 30] (* Harvey P. Dale, Feb 15 2016 *)

Prog

(Magma) I:=[1, 2, 3, 5, 48, 53, 101, 255, 10301, 20857, 31158, 52015, 499293, 551308, 1050601, 2652510]; [n le 16 select I[n] else 10402*Self(n-8)-Self(n-16): n in [1..50]]; // Vincenzo Librandi, Dec 24 2013

Crossrefs

Cf. A041790, A040395.

Sequence in context: A136371 A060380 A062608 * A322947 A056720 A100850

Adjacent sequences: A041788 A041789 A041790 * A041792 A041793 A041794

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 24 2013

Status

approved