A041979 Denominators of continued fraction convergents to sqrt(512).

1, 1, 2, 3, 8, 51, 569, 3465, 7499, 10964, 18463, 29427, 1313251, 1342678, 2655929, 3998607, 10653143, 67917465, 757745258, 4614389013, 9986523284, 14600912297, 24587435581, 39188347878, 1748874742213, 1788063090091, 3536937832304, 5325000922395

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1331714,0,0,0,0,0,0,0,0,0,0,0,-1).

Crossrefs

Cf. A041978, A040489.

Programs

Mathematica

Denominator[Convergents[Sqrt[512], 30]] (* Vincenzo Librandi, Jan 11 2014 *)

Formula

G.f.: -(x^22 -x^21 +2*x^20 -3*x^19 +8*x^18 -51*x^17 +569*x^16 -3465*x^15 +7499*x^14 -10964*x^13 +18463*x^12 -29427*x^11 -18463*x^10 -10964*x^9 -7499*x^8 -3465*x^7 -569*x^6 -51*x^5 -8*x^4 -3*x^3 -2*x^2 -x -1) / ((x^6 -34*x^3 +1)*(x^6 +34*x^3 +1)*(x^12 +1154*x^6 +1)). - Colin Barker, Nov 28 2013

Extensions

More terms from Colin Barker, Nov 28 2013