A042448 Numerators of continued fraction convergents to sqrt(752).

27, 55, 137, 192, 521, 713, 1947, 4607, 250725, 506057, 1262839, 1768896, 4800631, 6569527, 17939685, 42448897, 2310180123, 4662809143, 11635798409, 16298607552, 44233013513, 60531621065, 165296255643

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,9214,0,0,0,0,0,0,0,-1).

Formula

G.f.: (27 +55*x +137*x^2 +192*x^3 +521*x^4 +713*x^5 +1947*x^6 +4607*x^7 +1947*x^8 -713*x^9 +521*x^10 -192*x^11 +137*x^12 -55*x^13 +27*x^14 -x^15)/(1 -9214*x^8 +x^16). - Vincenzo Librandi, Nov 25 2013

a(n) = 9214*a(n-8) - a(n-16). - Vincenzo Librandi, Nov 25 2013

Mathematica

Numerator[Convergents[Sqrt[752], 30]] (* or *) CoefficientList[Series[(27 + 55 x + 137 x^2 + 192 x^3 + 521 x^4 + 713 x^5 + 1947 x^6 + 4607 x^7 + 1947 x^8 - 713 x^9 + 521 x^10 - 192 x^11 + 137 x^12 - 55 x^13 + 27 x^14 - x^15)/(1 - 9214 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 24 2013 *)

Prog

(Magma) I:=[27, 55, 137, 192, 521, 713, 1947, 4607, 250725, 506057, 1262839, 1768896, 4800631, 6569527, 17939685, 42448897]; [n le 16 select I[n] else 9214*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Nov 25 2013

Crossrefs

Cf. A042449.

Sequence in context: A042442 A042440 A190520 * A042446 A042450 A042452

Adjacent sequences: A042445 A042446 A042447 * A042449 A042450 A042451

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved