A041515 Denominators of continued fraction convergents to sqrt(274).

1, 1, 2, 9, 38, 47, 85, 2767, 2852, 5619, 25328, 106931, 132259, 239190, 7786339, 8025529, 15811868, 71273001, 300903872, 372176873, 673080745, 21910760713, 22583841458, 44494602171, 200562250142, 846743602739, 1047305852881, 1894049455620, 61656888432721

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,2814,0,0,0,0,0,0,1).

Formula

G.f.: -(x^12 -x^11 +2*x^10 -9*x^9 +38*x^8 -47*x^7 +85*x^6 +47*x^5 +38*x^4 +9*x^3 +2*x^2 +x +1) / (x^14 +2814*x^7 -1). - Colin Barker, Nov 18 2013

a(n) = 2814*a(n-7) + a(n-14) for n>13. - Vincenzo Librandi, Dec 19 2013

Mathematica

Denominator[Convergents[Sqrt[274], 30]] (* Vincenzo Librandi, Dec 19 2013 *)

Prog

(Magma) I:=[1, 1, 2, 9, 38, 47, 85, 2767, 2852, 5619, 25328, 106931, 132259, 239190]; [n le 14 select I[n] else 2814*Self(n-7)+Self(n-14): n in [1..30]]; // Vincenzo Librandi, Dec 19 2013

Crossrefs

Cf. A041514, A040257.

Sequence in context: A241454 A139102 A195187 * A010750 A026591 A007224

Adjacent sequences: A041512 A041513 A041514 * A041516 A041517 A041518

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved