A042755 Denominators of continued fraction convergents to sqrt(908).

1, 7, 8, 15, 218, 233, 451, 3390, 203851, 1430347, 1634198, 3064545, 44537828, 47602373, 92140201, 692583780, 41647167001, 292222752787, 333869919788, 626092672575, 9099167335838, 9725260008413, 18824427344251, 141496251418170, 8508599512434451

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,204302,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -7*x^13 +8*x^12 -15*x^11 +218*x^10 -233*x^9 +451*x^8 -3390*x^7 -451*x^6 -233*x^5 -218*x^4 -15*x^3 -8*x^2 -7*x -1) / ((x^8 -452*x^4 +1)*(x^8 +452*x^4 +1)). - Colin Barker, Dec 22 2013

a(n) = 204302*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Jan 28 2014

Mathematica

Denominator[Convergents[Sqrt[908], 30]] (* or *) LinearRecurrence[ {0, 0, 0, 0, 0, 0, 0, 204302, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 7, 8, 15, 218, 233, 451, 3390, 203851, 1430347, 1634198, 3064545, 44537828, 47602373, 92140201, 692583780}, 30] (* Harvey P. Dale, Jan 16 2014 *)

Prog

(Magma) I:=[1, 7, 8, 15, 218, 233, 451, 3390, 203851, 1430347, 1634198, 3064545, 44537828, 47602373, 92140201, 692583780]; [n le 16 select I[n] else 204302*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Jan 28 2014

Crossrefs

Cf. A042754, A040877.

Sequence in context: A041675 A041098 A041427 * A093083 A323418 A125195

Adjacent sequences: A042752 A042753 A042754 * A042756 A042757 A042758

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 22 2013

Status

approved