A042762 Numerators of continued fraction convergents to sqrt(912).

30, 151, 9090, 45601, 2745150, 13771351, 829026210, 4158902401, 250363170270, 1255974753751, 75608848395330, 379300216730401, 22833621852219390, 114547409477827351, 6895678190521860450, 34592938362087129601, 2082471979915749636510, 10446952837940835312151

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,302,0,-1).

Formula

G.f.: (30 +151*x +30*x^2 -x^3)/(1 -302*x^2 +x^4). - Vincenzo Librandi, Dec 04 2013

a(n) = 302*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 04 2013

Mathematica

Numerator[Convergents[Sqrt[912], 30]] (* or *) CoefficientList[Series[(30 + 151 x + 30 x^2 - x^3)/(1 - 302 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 04 2013 *)

Prog

(Magma) I:=[30, 151, 9090, 45601]; [n le 4 select I[n] else 302*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 04 2013

Crossrefs

Cf. A042763.

Sequence in context: A342483 A206040 A042760 * A368718 A064240 A141221

Adjacent sequences: A042759 A042760 A042761 * A042763 A042764 A042765

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 04 2013

Status

approved