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A087447
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a(0)=1,a(1)=1,a(n)=(n+2)*2^(n-2), n>1.
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8
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 21 2008]
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Aug 15 2010: (Start)
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).
(End)
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REFERENCES
| Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..3000
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FORMULA
| a(n)=sum{k=0..floor(n/2), C(n, 2k)(2k+1)}. - Paul Barry (pbarry(AT)wit.ie), Nov 29 2004
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MATHEMATICA
| Join[{1, 1}, Table[(n+2)2^(n-2), {n, 2, 30}]] (* From Harvey P. Dale, Feb 22 2011 *)
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CROSSREFS
| Essentially same as A079859.
Sequence in context: A090855 A052252 * A129953 A079859 A118871 A019494
Adjacent sequences: A087444 A087445 A087446 * A087448 A087449 A087450
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 05 2003
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EXTENSIONS
| Corrected definition by factor of 2 R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 21 2009
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