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Search: id:A120738
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| 0, 3, 7, 10, 15, 18, 22, 25, 31, 34, 38, 41, 46, 49, 53, 56, 63, 66, 70, 73, 78, 81, 85, 88, 94, 97, 101, 104, 109, 112, 116, 119, 127, 130, 134, 137, 142, 145, 149, 152, 158, 161, 165, 168, 173, 176, 180, 183, 190, 193, 197, 200, 205, 208, 212, 215, 221, 224, 228
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Partial sums of A090739. 2^a(n)=16^n/A001316(n)=A061549(n).
a(n) is also the increasing sequence of exponents of x in the \prod_{k > 1} (1 + x^(2^k - 1)) [From Paul Pearson (ppearson(AT)rochester.edu), Aug 06 2008]
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009: (Start)
2^a(n) = abs(A067624(n)/A117972(n))
(End)
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FORMULA
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a(n)=2n+A005187(n); a(n)=3n+A011371(n); a(n)=4n-log2(A001316(n)); a(n)=log2(A061549(n));
a(n) = A086343(n) + A001511(n) for n>0. [From Alford Arnold (Alford1940(AT)aol.com), Mar 23 2009]
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MAPLE
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a:=n->simplify(log[2](16^n/(add(modp(binomial(n, k), 2), k=0..n)))); a:=n->simplify(log[2](16^n/(2^(n-(padic[ordp](n!, 2)))))); # Note: n-(padic[ordp](n!, 2)) is the number of 1's in the binary expansion of n [From Paul Pearson (ppearson(AT)rochester.edu), Aug 06 2008]
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PROGRAM
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(PARI) {a(n) = if( n < 0, 0, 4*n - subst( Pol( binary( n ) ), x, 1) ) } /* Michael Somos Aug 28 2007 */
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CROSSREFS
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A086343 [From Alford Arnold (Alford1940(AT)aol.com), Mar 23 2009]
Sequence in context: A003231 A140487 A043722 this_sequence A085145 A143101 A121016
Adjacent sequences: A120735 A120736 A120737 this_sequence A120739 A120740 A120741
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jun 29 2006
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