A042284 Numerators of continued fraction convergents to sqrt(668).

25, 26, 155, 336, 4187, 8710, 47737, 56447, 2870087, 2926534, 17502757, 37932048, 472687333, 983306714, 5389220903, 6372527617, 324015601753, 330388129370, 1975956248603, 4282300626576, 53363563767515

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,112894,0,0,0,0,0,0,0,-1).

Formula

G.f.: (25 +26*x +155*x^2 +336*x^3 +4187*x^4 +8710*x^5 +47737*x^6 +56447*x^7 +47737*x^8 -8710*x^9 +4187*x^10 -336*x^11 +155*x^12 -26*x^13 +25*x^14 -x^15)/((1 -336*x^4 +x^8)*(1 +336*x^4 +x^8)). - Vincenzo Librandi, Nov 20 2013

a(n) = 112894*a(n-8) - a(n-16). - Vincenzo Librandi, Nov 18 2013

Mathematica

Numerator[Convergents[Sqrt[668], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 155 x^2 + 336 x^3 + 4187 x^4 + 8710 x^5 + 47737 x^6 + 56447 x^7 + 47737 x^8 - 8710 x^9 + 4187 x^10 - 336 x^11 + 155 x^12 - 26 x^13 + 25 x^14 - x^15)/(1 - 112894 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 20 2013 *)

Prog

(Magma) I:=[25, 26, 155, 336, 4187, 8710, 47737, 56447, 2870087, 2926534, 17502757, 37932048, 472687333, 983306714, 5389220903, 6372527617]; [n le 16 select I[n] else 112894*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Nov 18 2013

Crossrefs

Cf. A042285.

Sequence in context: A042276 A042282 A042280 * A042286 A042288 A042290

Adjacent sequences: A042281 A042282 A042283 * A042285 A042286 A042287

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved