A042454 Numerators of continued fraction convergents to sqrt(755).

27, 55, 577, 1209, 65863, 132935, 1395213, 2923361, 159256707, 321436775, 3373624457, 7068685689, 385082651663, 777233989015, 8157422541813, 17092079072641, 931129692464427, 1879351464001495

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, 2418, 0, 0, 0, -1).

Formula

G.f.: (27 +55*x +577*x^2 +1209*x^3 +577*x^4 -55*x^5 +27* x^6 -x^7)/(1 -2418*x^4 +x^8). - Vincenzo Librandi, Nov 25 2013

a(n) = 2418*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 25 2013

Mathematica

Numerator[Convergents[Sqrt[755], 40]] (* Harvey P. Dale, Feb 25 2012 *)
CoefficientList[Series[(27 + 55 x + 577 x^2 + 1209 x^3 + 577 x^4 - 55 x^5 + 27 x^6 - x^7)/(1 - 2418 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 25 2013 *)

Prog

(Magma) I:=[27, 55, 577, 1209, 65863, 132935, 1395213, 2923361]; [n le 8 select I[n] else 2418*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 25 2013

Crossrefs

Cf. A042455.

Sequence in context: A042446 A042450 A042452 * A042456 A132768 A352266

Adjacent sequences: A042451 A042452 A042453 * A042455 A042456 A042457

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved