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A041006 Numerators of continued fraction convergents to sqrt(6). 10
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

Hugo Pfoertner, Table of n, a(n) for n = 0..100

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,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Jun 10 2015

STATUS

approved

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Last modified August 23 00:23 EDT 2019. Contains 326211 sequences. (Running on oeis4.)