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A042448 Numerators of continued fraction convergents to sqrt(752). 2
27, 55, 137, 192, 521, 713, 1947, 4607, 250725, 506057, 1262839, 1768896, 4800631, 6569527, 17939685, 42448897, 2310180123, 4662809143, 11635798409, 16298607552, 44233013513, 60531621065, 165296255643 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 24 04:38 EDT 2019. Contains 324318 sequences. (Running on oeis4.)