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%I #48 Feb 12 2023 03:06:03
%S 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,
%T 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,
%U 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
%N a(n) = n-th partial sum of Golay-Rudin-Shapiro sequence A020985.
%H Reinhard Zumkeller, <a href="/A020986/b020986.txt">Table of n, a(n) for n = 0..10000</a>
%H John Brillhart and Patrick Morton, <a href="http://projecteuclid.org/euclid.ijm/1256048841">Über Summen von Rudin-Shapiroschen Koeffizienten</a>, (German) Illinois J. Math. 22 (1978), no. 1, 126--148. MR0476686 (57 #16245). - From _N. J. A. Sloane_, Jun 06 2012
%H J. Brillhart and P. Morton, <a href="http://www.maa.org/programs/maa-awards/writing-awards/a-case-study-in-mathematical-research-the-golay-rudin-shapiro-sequence">A case study in mathematical research: the Golay-Rudin-Shapiro sequence</a>, Amer. Math. Monthly, 103 (1996) 854-869.
%H Philip Lafrance, Narad Rampersad, and Randy Yee, <a href="http://arxiv.org/abs/1408.2277">Some properties of a Rudin-Shapiro-like sequence</a>, arXiv:1408.2277 [math.CO], 2014.
%H Narad Rampersad and Jeffrey Shallit, <a href="https://arxiv.org/abs/2302.00405">Rudin-Shapiro Sums Via Automata Theory and Logic</a>, arXiv:2302.00405 [math.NT], February 1 2023.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rudin-ShapiroSequence.html">Rudin-Shapiro Sequence</a>
%H <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F Brillhart and Morton (1978) list many properties.
%t 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 *)
%t Table[RudinShapiro[n], {n, 0, 100}] // Accumulate (* _Jean-François Alcover_, Jun 30 2022 *)
%o (Haskell)
%o a020986 n = a020986_list !! n
%o a020986_list = scanl1 (+) a020985_list
%o -- _Reinhard Zumkeller_, Jan 02 2012
%o (Python)
%o 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
%Y Cf. A020985, A020990.
%K nonn,nice
%O 0,2
%A _N. J. A. Sloane_
%E Minor edits by _N. J. A. Sloane_, Jun 06 2012
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