A041211 Denominators of continued fraction convergents to sqrt(116).

1, 1, 4, 9, 13, 61, 74, 209, 701, 910, 18901, 19811, 78334, 176479, 254813, 1195731, 1450544, 4096819, 13741001, 17837820, 370497401, 388335221, 1535503064, 3459341349, 4994844413, 23438719001, 28433563414, 80305845829, 269351100901, 349656946730

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,19602,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -x^17 +4*x^16 -9*x^15 +13*x^14 -61*x^13 +74*x^12 -209*x^11 +701*x^10 -910*x^9 -701*x^8 -209*x^7 -74*x^6 -61*x^5 -13*x^4 -9*x^3 -4*x^2 -x -1) / ((x^10 -140*x^5 -1)*(x^10 +140*x^5 -1)). - Colin Barker, Nov 14 2013

a(n) = 19602*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 13 2013

Mathematica

Denominator[Convergents[Sqrt[116], 30]]  (* Vincenzo Librandi, Dec 13 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 19602, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 4, 9, 13, 61, 74, 209, 701, 910, 18901, 19811, 78334, 176479, 254813, 1195731, 1450544, 4096819, 13741001, 17837820}, 30] (* Harvey P. Dale, Dec 14 2024 *)

Prog

(Magma) I:=[1, 1, 4, 9, 13, 61, 74, 209, 701, 910, 18901, 19811, 78334, 176479, 254813, 1195731, 1450544, 4096819, 13741001, 17837820]; [n le 20 select I[n] else 19602*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

Crossrefs

Cf. A041210, A010181.

Sequence in context: A041323 A319217 A041028 * A042323 A042083 A264733

Adjacent sequences: A041208 A041209 A041210 * A041212 A041213 A041214

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Corrected term of signature by Vincenzo Librandi, Dec 13 2013

Status

approved