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A087447
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a(0) = a(1) = 1; for n > 1, a(n) = (n+2)*2^(n-2).
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13
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1, 1, 4, 10, 24, 56, 128, 288, 640, 1408, 3072, 6656, 14336, 30720, 65536, 139264, 294912, 622592, 1310720, 2752512, 5767168, 12058624, 25165824, 52428800, 109051904, 226492416, 469762048, 973078528, 2013265920, 4160749568
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OFFSET
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0,3
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COMMENTS
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Binomial transform of A005408 (with interpolated zeros). Binomial transform is A087448. a(n+2) = 2*A045623(n+1); a(n+1) = A001792(n) + (0^n - (-2)^n)/2. The sequence 1,4,10,... given by 2^n*(n+3)/2 - 0^n/2 is the binomial transform of 1,3,3,5,5,...
Equals real part of binomial transform of [1, 2*i, 3, 4*i, 5, 6*i, ...]; i=sqrt(-1). - Gary W. Adamson, Sep 21 2008
An elephant sequence, see A175655. For the central square 24 A[5] vectors, with decimal values between 27 and 432, lead to this sequence (without the first leading 1). For the corner squares these vectors lead to the companion sequence A057711 (without the leading 0). - Johannes W. Meijer, Aug 15 2010
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LINKS
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FORMULA
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a(n) = Sum_{k=0..floor(n/2)} binomial(n, 2k)*(2k+1). - Paul Barry, Nov 29 2004
G.f.: (1-x)*(1-2*x+2*x^2)/(1-2*x)^2.
a(n) = 4*a(n-1) - 4*a(n-2) for n > 3. (End)
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MATHEMATICA
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Join[{1, 1}, Table[(n + 2) 2^(n - 2), {n, 2, 30}]] (* Harvey P. Dale, Feb 22 2011 *)
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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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EXTENSIONS
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Definition corrected (by a factor of 2) by R. J. Mathar, Feb 21 2009
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STATUS
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approved
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