A041549 Denominators of continued fraction convergents to sqrt(292).

1, 11, 23, 34, 125, 1034, 3227, 4261, 11749, 133500, 4550749, 50191739, 104934227, 155125966, 570312125, 4717622966, 14723181023, 19440803989, 53604789001, 609093483000, 20762783211001, 228999708804011, 478762200819023, 707761909623034, 2602047929688125

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,4562498,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -11*x^17 +23*x^16 -34*x^15 +125*x^14 -1034*x^13 +3227*x^12 -4261*x^11 +11749*x^10 -133500*x^9 -11749*x^8 -4261*x^7 -3227*x^6 -1034*x^5 -125*x^4 -34*x^3 -23*x^2 -11*x -1) / ((x^10 -2136*x^5 -1)*(x^10 +2136*x^5 -1)). - Colin Barker, Nov 22 2013

a(n) = 4562498*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[292], 30]] (* Vincenzo Librandi, Dec 20 2013 *)

Prog

(Magma) I:=[1, 11, 23, 34, 125, 1034, 3227, 4261, 11749, 133500, 4550749, 50191739, 104934227, 155125966, 570312125, 4717622966, 14723181023, 19440803989, 53604789001, 609093483000]; [n le 20 select I[n] else 4562498*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A041548, A040274.

Sequence in context: A208326 A097657 A041234 * A136771 A017653 A369463

Adjacent sequences: A041546 A041547 A041548 * A041550 A041551 A041552

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 22 2013

Status

approved