A041232 Numerators of continued fraction convergents to sqrt(128).

11, 34, 181, 577, 12875, 39202, 208885, 665857, 14857739, 45239074, 241053109, 768398401, 17145817931, 52205852194, 278175078901, 886731088897, 19786259034635, 60245508192802, 321013799998645

Offset

0,1

Links

Vincenzo Librandi and Bruno Berselli, Table of n, a(n) for n = 0..200 (first 151 terms from Vincenzo Librandi).

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1154,0,0,0,-1).

Formula

G.f.: (11 +34*x +181*x^2 +577*x^3 +181*x^4 -34*x^5 +11*x^6 -x^7) / ((1 -6*x +x^2)*(1 +6*x +x^2)*(1 +34*x^2 +x^4)). [Bruno Berselli, Oct 31 2013]

Mathematica

Numerator[Convergents[Sqrt[128], 30]] (* Vincenzo Librandi, Oct 31 2013 *)
LinearRecurrence[{0, 0, 0, 1154, 0, 0, 0, -1}, {11, 34, 181, 577, 12875, 39202, 208885, 665857}, 30] (* Bruno Berselli, Oct 31 2013 *)

Prog

(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((11+34*x+181*x^2+577*x^3+181*x^4-34*x^5+11*x^6-x^7)/((1-6*x+x^2)*(1+6*x+x^2)*(1+34*x^2+x^4)))); // Bruno Berselli, Oct 31 2013

Crossrefs

Cf. A041233.

Sequence in context: A300418 A041539 A233933 * A050287 A096762 A184207

Adjacent sequences: A041229 A041230 A041231 * A041233 A041234 A041235

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved