A041259 Denominators of continued fraction convergents to sqrt(141).

1, 1, 7, 8, 183, 191, 1329, 1520, 34769, 36289, 252503, 288792, 6605927, 6894719, 47974241, 54868960, 1255091361, 1309960321, 9114853287, 10424813608, 238460752663, 248885566271, 1731774150289, 1980659716560, 45306287914609, 47286947631169

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,190,0,0,0,-1).

Formula

G.f.: (1 +x +7*x^2 +8*x^3 -7*x^4 +x^5 -x^6)/(1-190*x^4 +x^8). - Vincenzo Librandi, Dec 14 2013

a(n) = 190*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 14 2013

Mathematica

Denominator[Convergents[Sqrt[141], 30]] (* or *) CoefficientList[Series[(1 + x + 7 x^2 + 8 x^3 - 7 x^4 + x^5 - x^6)/(1 - 190 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 14 2013 *)
LinearRecurrence[{0, 0, 0, 190, 0, 0, 0, -1}, {1, 1, 7, 8, 183, 191, 1329, 1520}, 30] (* Harvey P. Dale, Aug 28 2019 *)

Prog

(Magma) I:=[1, 1, 7, 8, 183, 191, 1329, 1520]; [n le 8 select I[n] else 190*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 14 2013

Crossrefs

Cf. A041258.

Sequence in context: A029496 A041109 A041110 * A371104 A041473 A041751

Adjacent sequences: A041256 A041257 A041258 * A041260 A041261 A041262

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Dec 14 2013

Status

approved