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A186949
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a(n) = 2^n - 2*(binomial(1,n) - binomial(0,n)).
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2
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1, 0, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824
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OFFSET
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0,3
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COMMENTS
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Second binomial transform is A186947.
Inverse binomial transform is (-1)^n * A168277(n).
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LINKS
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FORMULA
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G.f.: (1 - 2*x + 4*x^2)/(1-2*x).
a(n) = Sum_{k=0..n} binomial(n,k)*(3^k - 2*k).
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MAPLE
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MATHEMATICA
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Table[If[n<2, 1-n, 2^n], {n, 0, 30}] (* G. C. Greubel, Dec 01 2019 *)
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PROG
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(PARI) vector(31, n, if(n<3, 2-n, 2^(n-1))) \\ G. C. Greubel, Dec 01 2019
(Magma) [n lt 2 select 1-n else 2^n: n in [0..30]]; // G. C. Greubel, Dec 01 2019
(Sage) [1, 0]+[2^n for n in (2..30)] # G. C. Greubel, Dec 01 2019
(GAP) Concatenation([1, 0], List([2..30], n-> 2^n )); # G. C. Greubel, Dec 01 2019
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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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