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A082766 Series ratios converge alternately to sqrt(2) and 1+sqrt(1/2). 5
1, 1, 2, 3, 4, 7, 10, 17, 24, 41, 58, 99, 140, 239, 338, 577, 816, 1393, 1970, 3363, 4756, 8119, 11482, 19601, 27720, 47321, 66922, 114243, 161564, 275807, 390050, 665857, 941664, 1607521, 2273378, 3880899, 5488420, 9369319, 13250218, 22619537 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(2n+2)/a(2n+1) converges to sqrt(2).

a(2n+1)/a(2n) converges to 1+sqrt(1/2).

a(n+2)/a(n) converges to 1+sqrt(2).

a(2n) is A001333, a(2n+1) is A052542.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Haocong Song and Wen Wu, Hankel determinants of a Sturmian sequence, arXiv:2007.09940 [math.CO], 2020. See p. 4.

FORMULA

a(2n) = a(2n-1) + a(2n-2); a(2n+1) = a(2n) + a(2n-2)

O.g.f.: x*(1+x-x^2)*(x^2+1)/(1-2*x^2-x^4). - R. J. Mathar, Aug 08 2008

MATHEMATICA

Rest[CoefficientList[Series[x (1 - x^2 + x) (x^2 + 1)/(1 - 2 x^2 - x^4), {x, 0, 50}], x]] (* G. C. Greubel, Nov 28 2017 *)

PROG

(Haskell)

import Data.List (transpose)

a082766 n = a082766_list !! (n-1)

a082766_list = concat $ transpose [a052542_list, tail a001333_list]

-- Reinhard Zumkeller, Feb 24 2015

(PARI) x='x+O('x^30); Vec(x*(1+x-x^2)*(x^2+1)/(1-2*x^2-x^4)) \\ G. C. Greubel, Nov 28 2017

CROSSREFS

Cf. A001333, A052542. See A119016 for another version.

Sequence in context: A018143 A281839 A136570 * A119016 A082958 A218495

Adjacent sequences:  A082763 A082764 A082765 * A082767 A082768 A082769

KEYWORD

nonn

AUTHOR

Gary W. Adamson, May 24 2003

EXTENSIONS

Edited by Don Reble, Nov 04 2005

STATUS

approved

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Last modified April 18 03:59 EDT 2021. Contains 343072 sequences. (Running on oeis4.)