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A042674 Numerators of continued fraction convergents to sqrt(867). 2
29, 59, 265, 7744, 31241, 70226, 4104349, 8278924, 37220045, 1087660229, 4387860961, 9863382151, 576464025719, 1162791433589, 5227629760075, 152764054475764, 616283847663131, 1385331749802026, 80965525336180639 (list; graph; refs; listen; history; text; internal format)
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: A139507 A196940 A104119 * A078948 A269263 A042676

Adjacent sequences:  A042671 A042672 A042673 * A042675 A042676 A042677

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 23 07:41 EDT 2021. Contains 347609 sequences. (Running on oeis4.)