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A161204
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a(0)=2. a(n+1) = 2*a(n) + period 4: repeat -5,1,3,1.
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1
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2, -1, -1, 1, 3, 1, 3, 9, 19, 33, 67, 137, 275, 545, 1091, 2185, 4371, 8737, 17475, 34953, 69907, 139809, 279619, 559241, 1118483, 2236961, 4473923, 8947849, 17895699, 35791393, 71582787, 143165577, 286331155, 572662305, 1145324611, 2290649225, 4581298451, 9162596897
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: ( -2 + 3*x - x^3 + 2*x^2 ) / ( (2*x-1)*(1+x)*(1+x^2) ). - R. J. Mathar, Jan 26 2011
a(n) = a(n-4) + 2^(n-4).
a(n) = a(n-2) + (-3,2,4,0,0,8,16,24,=sixth differences of A007910(n-1) = 0,0,1,2,3,6,13 or fifth differences of A007909(n); also -3,2,4,8*A007910(n-1)).
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MAPLE
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A000034 := proc(n) if type(n, 'even') then 1 ; else 2 ; end if; end proc:
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MATHEMATICA
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CoefficientList[Series[(-2+3*x-x^3+2*x^2)/((2*x-1)*(1+x)*(1+x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 17 2012 *)
LinearRecurrence[{1, 1, 1, 2}, {2, -1, -1, 1}, 40] (* Harvey P. Dale, Dec 01 2019 *)
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PROG
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(Magma) I:=[2, -1, -1, 1]; [n le 4 select I[n] else Self(n-1)+Self(n-2)+Self(n-3)+2*Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 17 2012
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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