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A020986
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a(n) = n-th partial sum of Golay-Rudin-Shapiro sequence A020985.
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13
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1, 2, 3, 2, 3, 4, 3, 4, 5, 6, 7, 6, 5, 4, 5, 4, 5, 6, 7, 6, 7, 8, 7, 8, 7, 6, 5, 6, 7, 8, 7, 8, 9, 10, 11, 10, 11, 12, 11, 12, 13, 14, 15, 14, 13, 12, 13, 12, 11, 10, 9, 10, 9, 8, 9, 8, 9, 10, 11, 10, 9, 8, 9, 8, 9, 10, 11, 10, 11, 12, 11, 12, 13, 14, 15, 14, 13, 12, 13, 12, 13, 14, 15, 14, 15, 16
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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FORMULA
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Brillhart and Morton (1978) list many properties.
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MATHEMATICA
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a[n_] := 1 - 2 Mod[Length[FixedPointList[BitAnd[#, # - 1] &, BitAnd[n, Quotient[n, 2]]]], 2]; Accumulate@ Table[a@ n, {n, 0, 85}] (* Michael De Vlieger, Nov 30 2015, after Jan Mangaldan at A020985 *)
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PROG
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(Haskell)
a020986 n = a020986_list !! n
a020986_list = scanl1 (+) a020985_list
(Python)
def A020986(n): return sum(-1 if (m&(m>>1)).bit_count()&1 else 1 for m in range(n+1)) # Chai Wah Wu, Feb 11 2023
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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