A041751 Denominators of continued fraction convergents to sqrt(395).

1, 1, 7, 8, 311, 319, 2225, 2544, 98897, 101441, 707543, 808984, 31448935, 32257919, 224996449, 257254368, 10000662433, 10257916801, 71548163239, 81806080040, 3180179204759, 3261985284799, 22752090913553, 26014076198352, 1011286986450929, 1037301062649281

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, 318, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+8*x^2+1) / (x^8-318*x^4+1). - Colin Barker, Nov 23 2013

a(n) = 318*a(n-4) - a(n-8) for n>7, - Vincenzo Librandi, Dec 24 2013

Mathematica

Denominator[Convergents[Sqrt[395], 30]] (* Vincenzo Librandi, Dec 24 2013 *)
LinearRecurrence[{0, 0, 0, 318, 0, 0, 0, -1}, {1, 1, 7, 8, 311, 319, 2225, 2544}, 30] (* Harvey P. Dale, Dec 18 2022 *)

Prog

(Magma) I:=[1, 1, 7, 8, 311, 319, 2225, 2544]; [n le 8 select I[n] else 318*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 24 2013

Crossrefs

Cf. A041750, A040375.

Sequence in context: A041259 A371104 A041473 * A042093 A042499 A156206

Adjacent sequences: A041748 A041749 A041750 * A041752 A041753 A041754

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 23 2013

Status

approved