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A020986 a(n) = n-th partial sum of Golay-Rudin-Shapiro sequence A020985. 11
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)
OFFSET

0,2

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

John Brillhart and Patrick Morton, Über Summen von Rudin-Shapiroschen Koeffizienten, (German) Illinois J. Math. 22 (1978), no. 1, 126--148. MR0476686 (57 #16245). - From N. J. A. Sloane, Jun 06 2012

J. Brillhart and P. Morton, A case study in mathematical research: the Golay-Rudin-Shapiro sequence, Amer. Math. Monthly, 103 (1996) 854-869.

Philip Lafrance, Narad Rampersad, and Randy Yee, Some properties of a Rudin-Shapiro-like sequence, arXiv:1408.2277 [math.CO], 2014.

Eric Weisstein's World of Mathematics, Rudin-Shapiro Sequence

Index entries for sequences related to coordinates of 2D curves

FORMULA

Brillhart and Morton (1978) list many properties.

MATHEMATICA

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 *)

Table[RudinShapiro[n], {n, 0, 100}] // Accumulate (* Jean-François Alcover, Jun 30 2022 *)

PROG

(Haskell)

a020986 n = a020986_list !! n

a020986_list = scanl1 (+) a020985_list

-- Reinhard Zumkeller, Jan 02 2012

CROSSREFS

Cf. A020985.

Sequence in context: A045670 A194960 A111439 * A326820 A095161 A072106

Adjacent sequences:  A020983 A020984 A020985 * A020987 A020988 A020989

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

Minor edits by N. J. A. Sloane, Jun 06 2012

STATUS

approved

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Last modified September 27 15:39 EDT 2022. Contains 357062 sequences. (Running on oeis4.)