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A050493
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a(n) = sum of binary digits of n-th triangular number.
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2
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0, 1, 2, 2, 2, 4, 3, 3, 2, 4, 5, 2, 4, 5, 4, 4, 2, 4, 5, 6, 4, 6, 7, 3, 4, 4, 7, 6, 5, 6, 5, 5, 2, 4, 5, 6, 5, 8, 6, 4, 5, 7, 6, 6, 8, 4, 5, 4, 4, 5, 8, 6, 5, 7, 7, 3, 6, 7, 8, 7, 6, 7, 6, 6, 2, 4, 5, 6, 5, 8, 7, 8, 4, 6, 8, 5, 8, 9, 4, 5, 5, 8, 7, 8, 8, 7, 8, 8, 7, 8, 12, 5, 6, 5, 6, 5, 4, 5, 8, 7, 8
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{i=1..floor(log_b(c(n)))+1} (floor(c(n)/b^(i-1)) - floor(c(n)/b^i)*b), b=2, n >= 1, a(0)=0, c(n)=A000217(n).
a(n) = [x^(n*(n+1)/2)] (1/(1 - x))*Sum_{k>=0} x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Mar 27 2018
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MATHEMATICA
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Total[IntegerDigits[#, 2]]&/@Accumulate[Range[0, 100]] (* Harvey P. Dale, Jan 22 2012 *)
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PROG
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(Haskell)
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CROSSREFS
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KEYWORD
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base,easy,nice,nonn
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AUTHOR
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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 27 1999
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STATUS
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approved
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