A042669 Denominators of continued fraction convergents to sqrt(864).

1, 2, 3, 5, 28, 33, 457, 490, 2907, 3397, 6304, 16005, 934594, 1885193, 2819787, 4704980, 26344687, 31049667, 429990358, 461040025, 2735190483, 3196230508, 5931420991, 15059072490, 879357625411, 1773774323312, 2653131948723, 4426906272035, 24787663308898

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,940898,0,0,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^22 -2*x^21 +3*x^20 -5*x^19 +28*x^18 -33*x^17 +457*x^16 -490*x^15 +2907*x^14 -3397*x^13 +6304*x^12 -16005*x^11 -6304*x^10 -3397*x^9 -2907*x^8 -490*x^7 -457*x^6 -33*x^5 -28*x^4 -5*x^3 -3*x^2 -2*x -1) / ((x^4 -6*x^3 +13*x^2 -6*x +1)*(x^4 -10*x^2 +1)*(x^4 +10*x^2 +1)*(x^4 +6*x^3 +13*x^2 +6*x +1)*(x^8 +10*x^6 +99*x^4 +10*x^2 +1)). - Colin Barker, Dec 20 2013

a(n) = 940898*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[864], 30]] (* Vincenzo Librandi, Dec 20 2013 *)

Prog

(Magma) I:=[1, 2, 3, 5, 28, 33, 457, 490, 2907, 3397, 6304, 16005, 934594, 1885193, 2819787, 4704980, 26344687, 31049667, 429990358, 461040025, 2735190483, 3196230508, 5931420991, 15059072490]; [n le 24 select I[n] else 940898*Self(n-12)-Self(n-24): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A042668, A040834.

Sequence in context: A141566 A247094 A078736 * A178376 A041585 A042935

Adjacent sequences: A042666 A042667 A042668 * A042670 A042671 A042672

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 20 2013

Status

approved