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 A097581 a(n) = 3*2^floor((n-1)/2) + (-1)^n. 3
 2, 4, 5, 7, 11, 13, 23, 25, 47, 49, 95, 97, 191, 193, 383, 385, 767, 769, 1535, 1537, 3071, 3073, 6143, 6145, 12287, 12289, 24575, 24577, 49151, 49153, 98303, 98305, 196607, 196609, 393215, 393217, 786431, 786433, 1572863, 1572865 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Previous name was: a(1)=2 then if n even a(n)=a(n-1)+2 and if n odd a(n)=a(n-2)+a(n-1)-1. This sequence a(n)=A016116(n-1)+A086341(n). Generalization: starting with a(1) even then if n even a(n)=a(n-1)+2 and if n odd a(n)=a(n-2)+a(n-1)-1 you get a new sequence as a(1) increases. But if a(1) is odd, you get always the same sequence with only less values as a(1) increases. If a(1) is even, the sequence difference between two sequences with different but consecutive a(1) is the sequence of powers of 2 = 2,2,4,4,8,8,16,16,32,32,...... LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (-1,2,2). FORMULA From R. J. Mathar, Nov 13 2009: (Start) a(n) = -a(n-1) + 2*a(n-2) + 2*a(n-3). G.f.: x*(2+6*x+5*x^2)/((1+x)*(1-2*x^2)). (End) EXAMPLE Starting with a(1)=4 the new sequence is 4,6,9,11,19,21,39,41,79,81,159,161 The sequence difference between sequence starting with a(1)=4 and the sequence starting with a(1)=2 is 2,2,4,4,8,8,16,16,32,32,64,64,....... MATHEMATICA LinearRecurrence[{-1, 2, 2}, {2, 4, 5}, 40] (* Harvey P. Dale, Aug 10 2011 *) Table[3*2^(Floor[(n - 1)/2]) + (-1)^n, {n, 1, 50}] (* G. C. Greubel, Apr 18 2017 *) PROG (PARI) a(n)=3*2^floor((n-1)/2)+(-1)^n CROSSREFS Cf. A016116, A086341. Sequence in context: A307872 A239510 A039673 * A090614 A171022 A373030 Adjacent sequences: A097578 A097579 A097580 * A097582 A097583 A097584 KEYWORD nonn AUTHOR Pierre CAMI, Sep 20 2004 EXTENSIONS Equation in the comment corrected by R. J. Mathar, Nov 13 2009 Better name from Ralf Stephan, Aug 19 2013 STATUS approved

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Last modified September 13 20:16 EDT 2024. Contains 375910 sequences. (Running on oeis4.)