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A041006 Numerators of continued fraction convergents to sqrt(6). 9
2, 5, 22, 49, 218, 485, 2158, 4801, 21362, 47525, 211462, 470449, 2093258, 4656965, 20721118, 46099201, 205117922, 456335045, 2030458102, 4517251249, 20099463098, 44716177445, 198964172878, 442644523201, 1969542265682, 4381729054565, 19496458483942 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Interspersion of 2 sequences, 2*A054320 and A001079. - Gerry Martens, Jun 10 2015

LINKS

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (0,10,0,-1).

FORMULA

a(2n) = 2*A142238(2n) = A041038(2n)/2 ; a(2n-1) = A142238(2n-1) = A041038(2n-1) = A001079(n). [M. F. Hasler, Feb 13 2009]

G.f.: (2+5*x+2*x^2-x^3)/(1-10*x^2+x^4)

MATHEMATICA

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[6], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 16 2011*)

LinearRecurrence[{0, 10, 0, -1}, {2, 5, 22, 49}, 50] (* Vincenzo Librandi, Jun 10 2015 *)

PROG

(MAGMA) I:=[2, 5, 22, 49]; [n le 4 select I[n] else 10*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jun 10 2015

CROSSREFS

Cf. A041007.

Cf. A054320, A001079.

Sequence in context: A131510 A181443 A041165 * A288028 A083465 A215100

Adjacent sequences:  A041003 A041004 A041005 * A041007 A041008 A041009

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Jun 10 2015

STATUS

approved

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Last modified February 20 12:57 EST 2019. Contains 320327 sequences. (Running on oeis4.)