A042685 Denominators of continued fraction convergents to sqrt(872).

1, 1, 2, 15, 17, 236, 253, 2007, 2260, 4267, 249746, 254013, 503759, 3780326, 4284085, 59473431, 63757516, 505776043, 569533559, 1075309602, 62937490475, 64012800077, 126950290552, 952664833941, 1079615124493, 14987661452350, 16067276576843, 127458597490251

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, 252006, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^18 -x^17 +2*x^16 -15*x^15 +17*x^14 -236*x^13 +253*x^12 -2007*x^11 +2260*x^10 -4267*x^9 -2260*x^8 -2007*x^7 -253*x^6 -236*x^5 -17*x^4 -15*x^3 -2*x^2 -x -1) / ((x^10 -502*x^5 -1)*(x^10 +502*x^5 -1)). - Colin Barker, Dec 21 2013

a(n) = 252006*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 21 2013

Mathematica

Denominator/@Convergents[Sqrt[872], 30]  (* Harvey P. Dale, Mar 14 2011 *)
CoefficientList[Series[-(x^18 - x^17 + 2 x^16 - 15 x^15 + 17 x^14 - 236 x^13 + 253 x^12 - 2007 x^11 + 2260 x^10 - 4267 x^9 - 2260 x^8 - 2007 x^7 - 253 x^6 - 236 x^5 - 17 x^4 - 15 x^3 - 2 x^2 - x - 1)/((x^10 - 502 x^5 - 1) (x^10 + 502 x^5 - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 21 2013 *)

Prog

(Magma) I:=[1, 1, 2, 15, 17, 236, 253, 2007, 2260, 4267, 249746, 254013, 503759, 3780326, 4284085, 59473431, 63757516, 505776043, 569533559, 1075309602]; [n le 20 select I[n] else 252006*Self(n-10)-Self(n-20): n in [1..70]]; // Vincenzo Librandi, Dec 21 2013

Crossrefs

Cf. A042684, A040842.

Sequence in context: A041797 A041289 A249944 * A031022 A194542 A076646

Adjacent sequences: A042682 A042683 A042684 * A042686 A042687 A042688

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 21 2013

Status

approved