A042675 Denominators of continued fraction convergents to sqrt(867).

1, 2, 9, 263, 1061, 2385, 139391, 281167, 1264059, 36938878, 149019571, 334978020, 19577744731, 39490467482, 177539614659, 5188139292593, 20930096785031, 47048332862655, 2749733402819021, 5546515138500697, 24935793956821809, 728684539886333158

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, 140452, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^10 -2*x^9 +9*x^8 -263*x^7 +1061*x^6 -2385*x^5 -1061*x^4 -263*x^3 -9*x^2 -2*x -1) / ((x^4 -52*x^2 +1)*(x^8 +52*x^6 +2703*x^4 +52*x^2 +1)). - Colin Barker, Dec 20 2013

a(n) = 140452*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[867], 30]] (* Vincenzo Librandi, Dec 20 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 140452, 0, 0, 0, 0, 0, -1}, {1, 2, 9, 263, 1061, 2385, 139391, 281167, 1264059, 36938878, 149019571, 334978020}, 30] (* Harvey P. Dale, May 11 2024 *)

Prog

(Magma) I:=[1, 2, 9, 263, 1061, 2385, 139391, 281167, 1264059, 36938878, 149019571, 334978020]; [n le 12 select I[n] else 140452*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A042674, A040837.

Sequence in context: A165797 A011823 A122894 * A308647 A015177 A005271

Adjacent sequences: A042672 A042673 A042674 * A042676 A042677 A042678

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 20 2013

Status

approved