A042708 Numerators of continued fraction convergents to sqrt(884).

29, 30, 89, 119, 327, 446, 1219, 1665, 97789, 99454, 296697, 396151, 1088999, 1485150, 4059299, 5544449, 325637341, 331181790, 988000921, 1319182711, 3626366343, 4945549054, 13517464451, 18463013505, 1084372247741, 1102835261246, 3290042770233, 4392878031479

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,3330,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^15 -29*x^14 +30*x^13 -89*x^12 +119*x^11 -327*x^10 +446*x^9 -1219*x^8 -1665*x^7 -1219*x^6 -446*x^5 -327*x^4 -119*x^3 -89*x^2 -30*x -29) / (x^16 -3330*x^8 +1). - Colin Barker, Nov 09 2013

a(n) = 3330*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 02 2013

Mathematica

Numerator[Convergents[Sqrt[884], 30]] (* Harvey P. Dale, Nov 16 2011 *)
CoefficientList[Series[-(x^15 - 29 x^14 + 30 x^13 - 89 x^12 + 119 x^11 - 327 x^10 + 446 x^9 - 1219 x^8 - 1665 x^7 - 1219 x^6 - 446 x^5 - 327 x^4 - 119 x^3 - 89 x^2 - 30 x - 29)/(x^16 - 3330 x^8 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 02 2013 *)

Prog

(Magma) I:=[29, 30, 89, 119, 327, 446, 1219, 1665, 97789, 99454, 296697, 396151, 1088999, 1485150, 4059299, 5544449]; [n le 16 select I[n] else 3330*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Dec 02 2013

Crossrefs

Cf. A042709.

Sequence in context: A042684 A042682 A042706 * A042710 A042704 A042702

Adjacent sequences: A042705 A042706 A042707 * A042709 A042710 A042711

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 09 2013

Status

approved