A042264 Numerators of continued fraction convergents to sqrt(658).

25, 26, 51, 77, 513, 590, 1103, 1693, 85753, 87446, 173199, 260645, 1737069, 1997714, 3734783, 5732497, 290359633, 296092130, 586451763, 882543893, 5881715121, 6764259014, 12645974135, 19410233149

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, 3386, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (25 +26*x +51*x^2 +77*x^3 +513*x^4 +590*x^5 +1103*x^6 +1693*x^7 +1103*x^8 -590*x^9 +513*x^10 -77*x^11 +51*x^12 -26*x^13 +25*x^14 -x^15)/(1 -3386*x^8 +x^16). - Vincenzo Librandi, Nov 20 2013

a(n) = 3386*a(n-8) - a(n-16). - Vincenzo Librandi, Nov 18 2013

Mathematica

Numerator[Convergents[Sqrt[658], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 51 x^2 + 77 x^3 + 513 x^4 + 590 x^5 + 1103 x^6 + 1693 x^7 + 1103 x^8 - 590 x^9 + 513 x^10 - 77 x^11 + 51 x^12 - 26 x^13 + 25 x^14 - x^15)/(1 - 3386 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 20 2013 *)

Prog

(Magma) I:=[25, 26, 51, 77, 513, 590, 1103, 1693, 85753, 87446, 173199, 260645, 1737069, 1997714, 3734783, 5732497]; [n le 16 select I[n] else 3386*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Nov 18 2013

Crossrefs

Cf. A042265.

Sequence in context: A022395 A042260 A042262 * A274063 A042256 A042258

Adjacent sequences: A042261 A042262 A042263 * A042265 A042266 A042267

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved