A042232 Numerators of continued fraction convergents to sqrt(642).

25, 51, 76, 1875, 1951, 5777, 290801, 587379, 878180, 21663699, 22541879, 66747457, 3359914729, 6786576915, 10146491644, 250302376371, 260448868015, 771200112401, 38820454488065, 78412109088531

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,11554,0,0,0,0,0,-1).

Formula

G.f.: (25 +51*x +76*x^2 +1875*x^3 +1951*x^4 +5777*x^5 +1951*x^6 -1875*x^7 +76*x^8 -51*x^9 +25*x^10 -x^11)/(1 -11554*x^6 +x^12). - Vincenzo Librandi, Nov 19 2013

a(n) = 11554*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 19 2013

Mathematica

Numerator[Convergents[Sqrt[642], 30]] (* or *) CoefficientList[Series[(25 + 51 x + 76 x^2 + 1875 x^3 + 1951 x^4 + 5777 x^5 + 1951 x^6 - 1875 x^7 + 76 x^8 - 51 x^9 + 25 x^10 - x^11)/(1 - 11554 x^6 + x^12), {x, 0, 20}], x] (* Vincenzo Librandi, Nov 19 2013 *)

Prog

(Magma) I:=[25, 51, 76, 1875, 1951, 5777, 290801, 587379, 878180, 21663699, 22541879, 66747457]; [n le 12 select I[n] else 11554*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 19 2013

Crossrefs

Cf. A042233.

Sequence in context: A042236 A042238 A042234 * A273868 A338079 A337630

Adjacent sequences: A042229 A042230 A042231 * A042233 A042234 A042235

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved