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Search: id:A131572
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| A131572 |
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a(0)=0 and a(1)=1, continued such that absolute values of 2nd differences equal the original sequence. |
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+0
2
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| 0, 1, 2, 2, 4, 4, 8, 8, 16, 16, 32, 32, 64, 64, 128, 128, 256, 256, 512, 512, 1024, 1024, 2048, 2048, 4096, 4096, 8192, 8192, 16384, 16384, 32768, 32768
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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This is the main sequence of a family of sequences starting at a(0)=A and a(1)=B, continuing a(3,...)= 2B, 2B, 4B, 4B, 8B, 8B, 16B, 16B, 32B, 32B, .. such that the absolute values of the 2nd differences, |a(n+2)-2a(n+1)+a(n)|, equal the original sequence. Alternatively starting at a(0)=a(1)=1 gives A016116.
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FORMULA
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First differences: a(n+1)-a(n)=A131575(n). Second differences: A131575(n+1)-A131575(n)= (-1)^n*a(n).
a(n)=2a(n-2), n>2.
O.g.f.: x(1+2x)/(1-2x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 16 2008
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KEYWORD
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nonn,easy,new
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Aug 28 2007
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EXTENSIONS
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Edited by Richard J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 16 2008
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