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A041349 Denominators of continued fraction convergents to sqrt(188). 2
1, 1, 3, 7, 45, 97, 239, 336, 8975, 9311, 27597, 64505, 414627, 893759, 2202145, 3095904, 82695649, 85791553, 254278755, 594349063, 3820373133, 8235095329, 20290563791, 28525659120, 761957700911, 790483360031, 2342924420973, 5476332201977, 35200917632835 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,9214,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^14 -x^13 +3*x^12 -7*x^11 +45*x^10 -97*x^9 +239*x^8 -336*x^7 -239*x^6 -97*x^5 -45*x^4 -7*x^3 -3*x^2 -x -1) / ((x^8 -96*x^4 +1)*(x^8 +96*x^4 +1)). - Colin Barker, Nov 16 2013

a(n) = 9214*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 16 2013

MATHEMATICA

Denominator[Convergents[Sqrt[188], 30]] (* Vincenzo Librandi, Dec 16 2013 *)

PROG

(MAGMA) I:=[1, 1, 3, 7, 45, 97, 239, 336, 8975, 9311, 27597, 64505, 414627, 893759, 2202145, 3095904]; [n le 16 select I[n] else 9214*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013

CROSSREFS

Cf. A041348, A010230.

Sequence in context: A019011 A036842 A267844 * A041016 A301324 A184339

Adjacent sequences:  A041346 A041347 A041348 * A041350 A041351 A041352

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 16 2013

STATUS

approved

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Last modified February 26 03:09 EST 2020. Contains 332272 sequences. (Running on oeis4.)