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A167167
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A001045 with a(0) replaced by -1.
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2
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-1, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763, 349525, 699051, 1398101, 2796203, 5592405, 11184811, 22369621, 44739243, 89478485, 178956971, 357913941, 715827883, 1431655765, 2863311531
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OFFSET
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0,4
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COMMENTS
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Also the binomial transform of the sequence with terms (-1)^(n+1)*A128209(n).
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LINKS
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FORMULA
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G.f.: (2*x^2 + 2*x - 1)/((1+x)*(1-2*x)).
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MAPLE
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seq( `if`(n=0, -1, (2^n -(-1)^n)/3), n=0..35); # G. C. Greubel, Dec 01 2019
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MATHEMATICA
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CoefficientList[Series[(2*x-1+2*x^2)/((1+x)*(1-2*x)), {x, 0, 35}], x] (* G. C. Greubel, Jun 04 2016 *)
Table[If[n==0, -1, (2^n -(-1)^n)/3], {n, 0, 35}] (* G. C. Greubel, Dec 01 2019 *)
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PROG
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(PARI) vector(36, n, if(n==1, -1, (2^(n-1) +(-1)^n)/3 ) ) \\ G. C. Greubel, Dec 01 2019
(Magma) [-1] cat [(2^n -(-1)^n)/3): n in [1..35]]; // G. C. Greubel, Dec 01 2019
(Sage) [-1]+[lucas_number1(n, 1, -2) for n in (1..35)] # G. C. Greubel, Dec 01 2019
(GAP) Concatenation([-1], List([1..35], n-> (2^n -(-1)^n)/3) )); # G. C. Greubel, Dec 01 2019
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CROSSREFS
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KEYWORD
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sign,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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