A041705 Denominators of continued fraction convergents to sqrt(372).

1, 3, 7, 87, 181, 630, 24121, 72993, 170107, 2114277, 4398661, 15310260, 586188541, 1773875883, 4133940307, 51381159567, 106896259441, 372069937890, 14245553899261, 43108731635673, 100463017170607, 1248664937682957, 2597792892536521, 9042043615292520

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,24302,0,0,0,0,0,-1).

Formula

G.f.: -(x^10 -3*x^9 +7*x^8 -87*x^7 +181*x^6 -630*x^5 -181*x^4 -87*x^3 -7*x^2 -3*x -1) / ((x^4 -29*x^2 +1)*(x^8 +29*x^6 +840*x^4 +29*x^2 +1)). - Colin Barker, Nov 22 2013

a(n) = 24302*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[372], 30]] (* Vincenzo Librandi, Dec 23 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 24302, 0, 0, 0, 0, 0, -1}, {1, 3, 7, 87, 181, 630, 24121, 72993, 170107, 2114277, 4398661, 15310260}, 30] (* Harvey P. Dale, Nov 01 2025 *)

Prog

(Magma) I:=[1, 3, 7, 87, 181, 630, 24121, 72993, 170107, 2114277, 4398661, 15310260]; [n le 12 select I[n] else 24302*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 23 2013

Crossrefs

Cf. A041704, A040352.

Sequence in context: A219375 A326427 A064118 * A137130 A058379 A111002

Adjacent sequences: A041702 A041703 A041704 * A041706 A041707 A041708

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 22 2013

Status

approved