A042674 Numerators of continued fraction convergents to sqrt(867).

29, 59, 265, 7744, 31241, 70226, 4104349, 8278924, 37220045, 1087660229, 4387860961, 9863382151, 576464025719, 1162791433589, 5227629760075, 152764054475764, 616283847663131, 1385331749802026, 80965525336180639

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, 140452, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (29 +59*x +265*x^2 +7744*x^3 +31241*x^4 +70226*x^5 +31241*x^6 -7744*x^7 +265*x^8 -59*x^9 +29*x^10 -x^11)/(1 -140452*x^6 +x^12). - Vincenzo Librandi, Dec 01 2013

a(n) = 140452*a(n-6) - a(n-12). - Vincenzo Librandi, Dec 01 2013

Mathematica

Numerator[Convergents[Sqrt[867], 30]] (* or *) CoefficientList[Series[(29 + 59 x + 265 x^2 + 7744 x^3 + 31241 x^4 + 70226 x^5 + 31241 x^6 - 7744 x^7 + 265 x^8 - 59 x^9 + 29 x^10 - x^11)/(1 - 140452 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 01 2013 *)

Prog

(Magma) I:=[29, 59, 265, 7744, 31241, 70226, 4104349, 8278924, 37220045, 1087660229, 4387860961, 9863382151]; [n le 12 select I[n] else 140452*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Dec 01 2013

Crossrefs

Cf. A042675.

Sequence in context: A196940 A104119 A356717 * A078948 A269263 A042676

Adjacent sequences: A042671 A042672 A042673 * A042675 A042676 A042677

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved