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A097064
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Expansion of (1-4x+6x^2)/(1-2x)^2.
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6
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1, 0, 2, 8, 24, 64, 160, 384, 896, 2048, 4608, 10240, 22528, 49152, 106496, 229376, 491520, 1048576, 2228224, 4718592, 9961472, 20971520, 44040192, 92274688, 192937984, 402653184, 838860800, 1744830464, 3623878656, 7516192768, 15569256448, 32212254720, 66571993088
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OFFSET
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0,3
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COMMENTS
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Binomial transform of A097062.
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LINKS
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Table of n, a(n) for n=0..32.
Index entries for linear recurrences with constant coefficients, signature (4,-4).
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FORMULA
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a(n) = (n-1)*2^(n-1) + 3*0^n/2.
a(n) = 4*a(n-1) - 4*a(n-2), n>2.
a(n) = Sum_{k=0..n} binomial(n, k)*((2k-1)/2 + 3*(-1)^k/2).
a(n+1)/2 = A001787(n).
From Amiram Eldar, Oct 01 2022: (Start)
Sum_{n>=2} 1/a(n) = log(2) (A002162).
Sum_{n>=2} (-1)^n/a(n) = log(3/2) (A016578). (End)
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MATHEMATICA
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CoefficientList[Series[(1-4x+6x^2)/(1-2x)^2, {x, 0, 30}], x] (* or *) Join[{1}, LinearRecurrence[{4, -4}, {0, 2}, 30]] (* Harvey P. Dale, May 26 2011 *)
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CROSSREFS
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Essentially the same as A036289.
Cf. A001787, A002162, A016578.
Sequence in context: A292218 A134401 A036289 * A352206 A294458 A333186
Adjacent sequences: A097061 A097062 A097063 * A097065 A097066 A097067
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Jul 22 2004
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STATUS
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approved
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