A042593 Denominators of continued fraction convergents to sqrt(825).

1, 1, 3, 4, 7, 11, 18, 83, 101, 184, 285, 469, 1223, 1692, 95975, 97667, 291309, 388976, 680285, 1069261, 1749546, 8067445, 9816991, 17884436, 27701427, 45585863, 118873153, 164459016, 9328578049, 9493037065, 28314652179, 37807689244, 66122341423

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, 0, 0, 0, 0, 0, 0, 0, 0, 97198, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^26 -x^25 +3*x^24 -4*x^23 +7*x^22 -11*x^21 +18*x^20 -83*x^19 +101*x^18 -184*x^17 +285*x^16 -469*x^15 +1223*x^14 -1692*x^13 -1223*x^12 -469*x^11 -285*x^10 -184*x^9 -101*x^8 -83*x^7 -18*x^6 -11*x^5 -7*x^4 -4*x^3 -3*x^2 -x -1) / (x^28 -97198*x^14 +1). - Colin Barker, Dec 19 2013

a(n) = 97198*a(n-14) - a(n-28) for n>27. - Vincenzo Librandi, Jan 25 2014

Mathematica

Denominator[Convergents[Sqrt[825], 30]] (* Harvey P. Dale, Oct 16 2013 *)

Crossrefs

Cf. A042592, A040796.

Sequence in context: A041209 A293420 A041739 * A041018 A361907 A072255

Adjacent sequences: A042590 A042591 A042592 * A042594 A042595 A042596

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Dec 19 2013

Status

approved