A041461 Denominators of continued fraction convergents to sqrt(246).

1, 1, 3, 16, 19, 282, 301, 1787, 3875, 5662, 173735, 179397, 532529, 2842042, 3374571, 50086036, 53460607, 317389071, 688238749, 1005627820, 30857073349, 31862701169, 94582475687, 504775079604, 599357555291, 8895780853678, 9495138408969, 56371472898523

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,177610,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -x^17 +3*x^16 -16*x^15 +19*x^14 -282*x^13 +301*x^12 -1787*x^11 +3875*x^10 -5662*x^9 -3875*x^8 -1787*x^7 -301*x^6 -282*x^5 -19*x^4 -16*x^3 -3*x^2 -x -1) / (x^20 -177610*x^10 +1). - Colin Barker, Nov 18 2013

a(n) = 177610*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 18 2013

Mathematica

Denominator[Convergents[Sqrt[246], 30]] (* Vincenzo Librandi, Dec 18 2013 *)

Prog

(Magma) I:=[1, 1, 3, 16, 19, 282, 301, 1787, 3875, 5662, 173735, 179397, 532529, 2842042, 3374571, 50086036, 53460607, 317389071, 688238749, 1005627820]; [n le 20 select I[n] else 177610*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 18 2013

Crossrefs

Cf. A041460, A040230.

Sequence in context: A042075 A342716 A042777 * A277724 A175285 A031071

Adjacent sequences: A041458 A041459 A041460 * A041462 A041463 A041464

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved