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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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4
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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, 65536, 65536, 131072, 131072, 262144, 262144, 524288, 524288, 1048576, 1048576
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OFFSET
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0,3
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COMMENTS
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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, abs(a(n+2)-2*a(n+1)+a(n)), equal the original sequence. Alternatively starting at a(0)=a(1)=1 gives A016116.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (0,2).
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FORMULA
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a(n) = 2*a(n-2), n>2.
O.g.f.: x*(1+2*x)/(1-2*x^2). - R. J. Mathar, Jul 16 2008
a(n) = A016116(n) - A000007(n), that is, a(0)=0, a(n)=A016116(n) for n>=1 - Bruno Berselli, Apr 13 2011
First differences: a(n+1)-a(n)=A131575(n).
Second differences: A131575(n+1)-A131575(n)= (-1)^n*a(n).
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MATHEMATICA
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LinearRecurrence[{0, 2}, {0, 1, 2}, 50] (* Harvey P. Dale, Jul 10 2018 *)
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PROG
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(MAGMA) [2^Floor(n/2)-0^n: n in [0..50]]; // Vincenzo Librandi, Aug 18 2011
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CROSSREFS
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Sequence in context: A076939 A158780 A117575 * A152166 A320770 A016116
Adjacent sequences: A131569 A131570 A131571 * A131573 A131574 A131575
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Curtz, Aug 28 2007
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EXTENSIONS
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Edited by R. J. Mathar, Jul 16 2008
More terms from Vincenzo Librandi, Aug 18 2011
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STATUS
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approved
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