A041045 Denominators of continued fraction convergents to sqrt(28).

1, 3, 7, 24, 247, 765, 1777, 6096, 62737, 194307, 451351, 1548360, 15934951, 49353213, 114641377, 393277344, 4047414817, 12535521795, 29118458407, 99890897016, 1028027428567, 3183973182717, 7395973794001

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,254,0,0,0,-1).

Crossrefs

Cf. A010479, A041044.

Programs

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[28], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011 *)
CoefficientList[Series[- (x^2 - 3 x - 1) (x^4 + 8 x^2 + 1)/((x^4 - 16 x^2 + 1) (x^4 + 16 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 23 2013 *)
LinearRecurrence[{0,0,0,254,0,0,0,-1},{1,3,7,24,247,765,1777,6096},30] (* or *) Denominator[Convergents[Sqrt[28],30]] (* Harvey P. Dale, Nov 29 2024 *)

Formula

a(n) = 254*a(n-4)-a(n-8). G.f.: -(x^2-3*x-1)*(x^4+8*x^2+1)/((x^4-16*x^2+1)*(x^4+16*x^2+1)). [Colin Barker, Jul 16 2012]