A041092 Numerators of continued fraction convergents to sqrt(54).

7, 15, 22, 147, 169, 485, 6959, 14403, 21362, 142575, 163937, 470449, 6750223, 13970895, 20721118, 138297603, 159018721, 456335045, 6547709351, 13551753747, 20099463098, 134148532335, 154247995433

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,970,0,0,0,0,0,-1).

Crossrefs

Cf. A010507, A041093.

Programs

Mathematica

Numerator[Convergents[Sqrt[54],30]] (* Harvey P. Dale, Jul 18 2013 *)
CoefficientList[Series[- (x^11 - 7 x^10 + 15 x^9 - 22 x^8 + 147 x^7 - 169 x^6 - 485 x^5 - 169 x^4 - 147 x^3 - 22 x^2 - 15 x - 7)/((x^4 - 10 x^2 + 1) (x^8 + 10 x^6 + 99 x^4 + 10 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 25 2013 *)

Formula

a(n) = 970*a(n-6)-a(n-12). G.f.: -(x^11-7*x^10+15*x^9-22*x^8+147*x^7-169*x^6-485*x^5-169*x^4-147*x^3-22*x^2-15*x-7)/((x^4-10*x^2+1)*(x^8+10*x^6+99*x^4+10*x^2+1)). [Colin Barker, Jul 18 2012]