A041595 Denominators of continued fraction convergents to sqrt(315).

1, 1, 3, 4, 139, 143, 425, 568, 19737, 20305, 60347, 80652, 2802515, 2883167, 8568849, 11452016, 397937393, 409389409, 1216716211, 1626105620, 56504307291, 58130412911, 172765133113, 230895546024, 8023213697929, 8254109243953, 24531432185835, 32785541429788

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,142,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+4*x^2+1) / ((x^4-12*x^2+1)*(x^4+12*x^2+1)). - Colin Barker, Nov 19 2013

a(n) = 142*a(n-4) - a(n-8) for n>7, - Vincenzo Librandi, Dec 21 2013

Mathematica

Denominator[Convergents[Sqrt[315], 30]] (* Vincenzo Librandi, Dec 21 2013 *)

Prog

(Magma) I:=[1, 1, 3, 4, 139, 143, 425, 568]; [n le 8 select I[n] else 142*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 21 2013

Crossrefs

Cf. A041594, A040297.

Sequence in context: A331815 A077032 A370385 * A041741 A041903 A156513

Adjacent sequences: A041592 A041593 A041594 * A041596 A041597 A041598

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 19 2013

Status

approved