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A132720
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Sequence is identical to its second differences in absolute values.
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1
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1, 2, 4, 8, 8, 16, 32, 32, 64, 128, 128, 256, 512, 512, 1024, 2048, 2048, 4096, 8192, 8192, 16384, 32768, 32768, 65536, 131072, 131072, 262144, 524288, 524288, 1048576, 2097152, 2097152, 4194304, 8388608, 8388608, 16777216, 33554432, 33554432, 67108864, 134217728, 134217728, 268435456, 536870912, 536870912
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OFFSET
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0,2
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LINKS
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FORMULA
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After 1, 2, repeat 4^p, 2*4^p, 2*4^p, p positive.
G.f.: 1 + 2*x*(1 +2*x +4*x^2)/(1 - 4*x^3). - R. J. Mathar, Nov 07 2015
a(2*n+1) = 2^floor((4*n+1)/3) = 2^A042965(n+1).
a(2*n) = 2^floor((2*n+3)/3)) = 2^A042968(n), n >= 1. (End)
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MATHEMATICA
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Join[{1}, LinearRecurrence[{0, 0, 4}, {2, 4, 8}, 45]] (* Ray Chandler, Sep 23 2015 *)
Table[If[EvenQ[n], 2^Floor[(2*n+3)/3] - Boole[n==0], 2^Floor[(2*n+3)/3]], {n, 0, 45}] (* G. C. Greubel, Feb 15 2021 *)
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PROG
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(Sage)
def A132170(n): return 2^floor((2*n+3)/3) if n%2==0 else 2^floor((2*n+3)/3)
(Magma)
A132170:= func< n | n eq 0 select 1 else (n mod 2 eq 0) select 2^Floor((2*n+3)/3) else 2^Floor((2*n+3)/3) >;
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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