A042398 Numerators of continued fraction convergents to sqrt(726).

26, 27, 458, 485, 25678, 26163, 444286, 470449, 24907634, 25378083, 430956962, 456335045, 24160379302, 24616714347, 418027808854, 442644523201, 23435543015306, 23878187538507, 405486543631418

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, 970, 0, 0, 0, -1).

Formula

G.f.: (26+27* x+458* x^2+485*x^3+458*x^4-27*x^5+26*x^6-x^7)/(1-970*x^4+x^8). - Vincenzo Librandi, Nov 23 2013

a(n) = 970*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 23 2013

Mathematica

Numerator[Convergents[Sqrt[726], 30]] (* or *) CoefficientList[Series[(26 + 27 x + 458 x^2 + 485 x^3 + 458 x^4 - 27 x^5 + 26 x^6 - x^7)/(1 - 970 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 23 2013 *)
LinearRecurrence[{0, 0, 0, 970, 0, 0, 0, -1}, {26, 27, 458, 485, 25678, 26163, 444286, 470449}, 30] (* Harvey P. Dale, Nov 27 2022 *)

Prog

(Magma) I:=[26, 27, 458, 485, 25678, 26163, 444286, 470449]; [n le 8 select I[n] else 970*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 23 2013

Crossrefs

Cf. A042399.

Sequence in context: A137118 A137119 A042396 * A042400 A042401 A042402

Adjacent sequences: A042395 A042396 A042397 * A042399 A042400 A042401

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved