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A041791 Denominators of continued fraction convergents to sqrt(416). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 23 12:38 EDT 2019. Contains 323514 sequences. (Running on oeis4.)