A041213 Denominators of continued fraction convergents to sqrt(117).

1, 1, 5, 11, 49, 60, 1249, 1309, 6485, 14279, 63601, 77880, 1621201, 1699081, 8417525, 18534131, 82554049, 101088180, 2104317649, 2205405829, 10925940965, 24057287759, 107155092001, 131212379760

Offset

0,3

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

From Colin Barker, Jul 19 2012: (Start)

a(n) = 1298*a(n-6) - a(n-12).

G.f.: -(x^10 - x^9 + 5*x^8 - 11*x^7 + 49*x^6 - 60*x^5 - 49*x^4 - 11*x^3 - 5*x^2 - x - 1)/((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)). (End)

Mathematica

Denominator[Convergents[Sqrt[117], 30]] (* Vincenzo Librandi, Oct 24 2013 *)

Crossrefs

Cf. A041212, A010182.

Sequence in context: A097743 A350648 A176609 * A142238 A370769 A149514

Adjacent sequences: A041210 A041211 A041212 * A041214 A041215 A041216

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved