A041495 Denominators of continued fraction convergents to sqrt(264).

1, 4, 129, 520, 16769, 67596, 2179841, 8786960, 283362561, 1142237204, 36834953089, 148482049560, 4788260539009, 19301524205596, 622437035118081, 2509049664677920, 80912026304811521, 326157154883924004, 10517940982590379649, 42397921085245442600

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,130,0,-1).

Formula

G.f.: (1+4*x-x^2)/(1-130*x^2+x^4). - Colin Barker, Nov 18 2013

a(n) = 130*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 18 2013

a(2n) = A041115(2n), a(2n+1) = A041115(2n+1)/2. - M. F. Hasler, Feb 24 2020

Mathematica

Denominator[Convergents[Sqrt[264], 30]] (* Vincenzo Librandi, Dec 18 2013 *)

Prog

(Magma) I:=[1, 4, 129, 520]; [n le 4 select I[n] else 130*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 18 2013
(PARI) apply( {A041495(n)=([130, -1; 1, 0]^(n\2))[1, ]*[4^n%=2, 1-n]~}, [0..20]) \\ M. F. Hasler, Feb 24 2020

Crossrefs

Cf. A040247, A041115, A041494.

Sequence in context: A146555 A305568 A057134 * A188315 A298274 A299136

Adjacent sequences: A041492 A041493 A041494 * A041496 A041497 A041498

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved