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A133684 a(2n) = A001045(n); a(1)=1; a(2n+1) = 2*A001045(n-1) for n >= 1. 2
0, 1, 1, 0, 1, 2, 3, 2, 5, 6, 11, 10, 21, 22, 43, 42, 85, 86, 171, 170, 341, 342, 683, 682, 1365, 1366, 2731, 2730, 5461, 5462, 10923, 10922, 21845, 21846, 43691, 43690, 87381, 87382, 174763, 174762, 349525, 349526, 699051, 699050, 1398101, 1398102, 2796203, 2796202 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,1,0,2).

FORMULA

a(4*n) + a(4*n+1) = a(4*n+2).

a(n) + a(n+2) = 2^floor(n/2) = A016116(n).

O.g.f.: x - x^2*(1 + 2*x^3)/((2*x^2-1)*(x^2+1)) . - R. J. Mathar, Feb 23 2008

PROG

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 2, 0, 1, 0]^n*[0; 1; 1; 0])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016

CROSSREFS

Cf. A001045, A016116, A133730 (first differences).

Sequence in context: A211506 A182880 A182898 * A286151 A192138 A175264

Adjacent sequences: A133681 A133682 A133683 * A133685 A133686 A133687

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Jan 04 2008

EXTENSIONS

Terms a(24) and beyond from Andrew Howroyd, Feb 02 2020

STATUS

approved

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Last modified February 5 03:48 EST 2023. Contains 360082 sequences. (Running on oeis4.)