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A049610
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Sum( k*binomial(n,2*k), 0 <= k <= n/2) = floor( n*2^(n-3) ).
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1
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0, 0, 1, 3, 8, 20, 48, 112, 256, 576, 1280, 2816, 6144, 13312, 28672, 61440, 131072, 278528, 589824, 1245184, 2621440, 5505024, 11534336, 24117248, 50331648, 104857600, 218103808, 452984832, 939524096, 1946157056, 4026531840
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OFFSET
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0,4
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COMMENTS
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Essentially same as A001792, except for leading zeros, which motivate the existence of this sequence on its own.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
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G.f. x^2*(1-x)/(1-2*x)^2. - Sergei N. Gladkovskii, Oct 18 2012
G.f.: x^2*( 1 + 2*x*U(0) ) where U(k)= 1 + (k+1)/(2 - 8*x/(4*x + (k+1)/U(k+1))) ; (continued fraction, 3-step). - Sergei N. Gladkovskii, Oct 19 2012
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MATHEMATICA
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CoefficientList[Series[x^2*(1 - x)/(1 - 2*x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 09 2013
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PROG
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(PARI) a(n)=n<<(n-3)
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CROSSREFS
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Cf. A189162, A189390, A189391.
Sequence in context: A143662 A151975 A001792 * A168150 A018795 A018794
Adjacent sequences: A049607 A049608 A049609 * A049611 A049612 A049613
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KEYWORD
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nonn,easy
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AUTHOR
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M. F. Hasler, Jan 25 2012
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STATUS
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approved
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