A042469 Denominators of continued fraction convergents to sqrt(762).

1, 1, 2, 3, 5, 43, 48, 91, 139, 230, 12559, 12789, 25348, 38137, 63485, 546017, 609502, 1155519, 1765021, 2920540, 159474181, 162394721, 321868902, 484263623, 806132525, 6933323823, 7739456348, 14672780171, 22412236519, 37085016690, 2025003137779

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, 12698, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^4 - 3*x^3 + 4*x^2 - 2*x + 1)*(x^4 + 2*x^3 + 4*x^2 + 3*x + 1)*(x^10 - 46*x^5 - 1) / (x^20 - 12698*x^10 + 1). - Colin Barker, Dec 15 2013

a(n) = 12698*a(n-10) - a(n-20) for n > 19. - Vincenzo Librandi, Jan 23 2014

Mathematica

Denominator[Convergents[Sqrt[762], 30]] (* Harvey P. Dale, Feb 20 2013 *)

Prog

(Magma) I:=[1, 1, 2, 3, 5, 43, 48, 91, 139, 230, 12559, 12789, 25348, 38137, 63485, 546017, 609502, 1155519, 1765021, 2920540]; [n le 20 select I[n] else 12698*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Jan 23 2014

Crossrefs

Cf. A042468, A040734.

Sequence in context: A106713 A106820 A362957 * A107990 A117460 A281252

Adjacent sequences: A042466 A042467 A042468 * A042470 A042471 A042472

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Dec 15 2013

Status

approved