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A181586
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a(0)=0; a(n+1) = 2*a(n) + period 4:repeat 0,1,-2,1.
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1
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0, 0, 1, 0, 1, 2, 5, 8, 17, 34, 69, 136, 273, 546, 1093, 2184, 4369, 8738, 17477, 34952, 69905, 139810, 279621, 559240, 1118481, 2236962, 4473925, 8947848, 17895697, 35791394, 71582789, 143165576, 286331153, 572662306, 1145324613, 2290649224
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OFFSET
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0,6
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COMMENTS
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a(n) + a(n+1) + a(n+2) + a(n+3) = 2^n.
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LINKS
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FORMULA
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a(n) = a(n-4) + 2^(n-4).
a(n) = a(n-2) + A118405(n-2) unsigned.
a(n) = a(n-1) + a(n-2) + a(n-3) + 2*a(n-4) (**).
G.f. x^2*(-1+x) / ( (2*x-1)*(1+x)*(x^2+1) ). - R. J. Mathar, Feb 06 2011
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EXAMPLE
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a(1)=2*a(0)+0=0, a(2)=2*a(1)+1=0+1=1, a(3)=2*a(2)-2=2-2=0, a(4)=2*a(3)+1=0+1=1, a(5)=2*a(4)+0=2+0=2, a(6)=2*a(5)+1=4+1=5.
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MAPLE
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a:= proc(n) option remember;
`if`(n=0, 0, 2*a(n-1) +[0, 1, -2, 1][irem(n-1, 4)+1])
end:
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MATHEMATICA
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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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STATUS
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approved
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