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A020986 a(n) = n-th partial sum of Golay-Rudin-Shapiro sequence A020985. 6
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, 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, 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

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 *)

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 * A095161 A072106 A124524

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 December 8 11:12 EST 2016. Contains 278939 sequences.