A042742 Numerators of continued fraction convergents to sqrt(902).

30, 901, 54090, 1623601, 97470150, 2925728101, 175641156210, 5272160414401, 316505266020270, 9500430141022501, 570342313727370330, 17119769841962132401, 1027756532831455314390, 30849815754785621564101, 1852016701819968749160450, 55591350870353848096377601

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,1802,0,-1).

Formula

G.f.: -(x^3-30*x^2-901*x-30) / (x^4-1802*x^2+1). - Vincenzo Librandi, Dec 03 2013, simplified by Colin Barker, Dec 27 2013

a(n) = 1802*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 03 2013, simplified by Colin Barker, Dec 27 2013

Mathematica

Numerator[Convergents[Sqrt[902], 30]] (* or *) CoefficientList[Series[(30 + 901 x + 30 x^2 - x^3)/(1 - 1802 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2013 *)

Prog

(Magma) I:=[30, 901, 54090, 1623601]; [n le 4 select I[n] else 1802*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 03 2013

Crossrefs

Cf. A042743, A040871.

Sequence in context: A171304 A009974 A041421 * A144350 A111216 A158672

Adjacent sequences: A042739 A042740 A042741 * A042743 A042744 A042745

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 03 2013

Status

approved