A041349 Denominators of continued fraction convergents to sqrt(188).

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

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: A036842 A267844 A359046 * A041016 A351354 A365572

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