A041088 Numerators of continued fraction convergents to sqrt(52).

7, 29, 36, 101, 137, 649, 9223, 37541, 46764, 131069, 177833, 842401, 11971447, 48728189, 60699636, 170127461, 230827097, 1093435849, 15538928983, 63249151781, 78788080764, 220825313309, 299613394073

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1298,0,0,0,0,0,-1).

Formula

a(n) = 1298*a(n-6)-a(n-12). G.f.: -(x^11-7*x^10+29*x^9-36*x^8+101*x^7-137*x^6-649*x^5-137*x^4-101*x^3-36*x^2-29*x-7)/((x^2-3*x-1)*(x^2+3*x-1)*(x^4-3*x^3+10*x^2+3*x+1)*(x^4+3*x^3+10*x^2-3*x+1)). [Colin Barker, Jul 18 2012]

Mathematica

Numerator[Convergents[Sqrt[52], 30]] (* Vincenzo Librandi, Oct 25 2013 *)

Crossrefs

Cf. A010505, A041089.

Sequence in context: A140447 A038934 A262285 * A107923 A096450 A156124

Adjacent sequences: A041085 A041086 A041087 * A041089 A041090 A041091

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved