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Search: id:A087447
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| A087447 |
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a(0)=1,a(1)=1,a(n)=2^n(n+2)/2, n>1. |
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+0
5
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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; listen)
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OFFSET
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0,3
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COMMENT
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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). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 21 2008]
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REFERENCES
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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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FORMULA
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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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CROSSREFS
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Essentially same as A079859.
Adjacent sequences: A087444 A087445 A087446 this_sequence A087448 A087449 A087450
Sequence in context: A097976 A090855 A052252 this_sequence A129953 A079859 A118871
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KEYWORD
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easy,nonn,new
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 05 2003
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