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A041266 Numerators of continued fraction convergents to sqrt(146). 2
12, 145, 3492, 42049, 1012668, 12194065, 293670228, 3536236801, 85163353452, 1025496478225, 24697078830852, 297390442448449, 7162067697593628, 86242202813571985, 2076974935223321268, 25009941425493427201, 602315569147065574092, 7252796771190280316305 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..811

Index entries for linear recurrences with constant coefficients, signature (0,290,0,-1).

FORMULA

G.f.: (12+145*x+12*x^2-x^3)/(1-290*x^2+x^4); // Vincenzo Librandi, Nov 01 2013

a(n) = 290*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 01 2013

MATHEMATICA

Numerator[Convergents[Sqrt[146], 30]] (* or *) CoefficientList[Series[(12 + 145 x + 12 x^2 - x^3)/(1 - 290 x^2 + x^4), {x, 0, 25}], x] (* Vincenzo Librandi, Oct 31 2013 *)

LinearRecurrence[{0, 290, 0, -1}, {12, 145, 3492, 42049}, 20] (* Harvey P. Dale, May 11 2017 *)

PROG

(MAGMA) I:=[12, 145, 3492, 42049]; [n le 4 select I[n] else 290*Self(n-2)-Self(n-4): n in [1..20]]; // Vincenzo Librandi, Nov 01 2013

CROSSREFS

Cf. A041267.

Sequence in context: A288792 A041061 A174227 * A015501 A039493 A196454

Adjacent sequences:  A041263 A041264 A041265 * A041267 A041268 A041269

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Harvey P. Dale, May 11 2017

STATUS

approved

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Last modified December 5 06:52 EST 2021. Contains 349543 sequences. (Running on oeis4.)