A042180 Numerators of continued fraction convergents to sqrt(615).

24, 25, 99, 124, 6051, 6175, 24576, 30751, 1500624, 1531375, 6094749, 7626124, 372148701, 379774825, 1511473176, 1891248001, 92291377224, 94182625225, 374839252899, 469021878124, 22887889402851, 23356911280975

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,248,0,0,0,-1).

Formula

G.f.: (24 +25*x +99*x^2 +124*x^3 +99*x^4 -25*x^5 +24*x^6 -x^7)/(1 -248*x^4 +x^8). - Vincenzo Librandi, Nov 18 2013

a(n) = 248*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 18 2013

Mathematica

Numerator[Convergents[Sqrt[615], 30]] (* or *) CoefficientList[Series[(24 + 25 x + 99 x^2 + 124 x^3 + 99*x^4 - 25 x^5 + 24 x^6 - x^7)/(1 - 248 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 18 2013 *)

Prog

(Magma) I:=[24, 25, 99, 124, 6051, 6175, 24576, 30751]; [n le 8 select I[n] else 248*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 18 2013

Crossrefs

Cf. A042181.

Sequence in context: A042170 A042168 A042178 * A042176 A042182 A042184

Adjacent sequences: A042177 A042178 A042179 * A042181 A042182 A042183

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved