

A020986


a(n) = nth partial sum of GolayRudinShapiro sequence A020985.


8



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
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OFFSET

0,2


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
John Brillhart, Patrick Morton, Über Summen von RudinShapiroschen Koeffizienten, (German) Illinois J. Math. 22 (1978), no. 1, 126148. MR0476686 (57 #16245).  From N. J. A. Sloane, Jun 06 2012
J. Brillhart and P. Morton, A case study in mathematical research: the GolayRudinShapiro sequence, Amer. Math. Monthly, 103 (1996) 854869.
Philip Lafrance, Narad Rampersad, Randy Yee, Some properties of a RudinShapirolike sequence, arXiv:1408.2277 [math.CO], 2014.
Eric Weisstein's World of Mathematics, RudinShapiro 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 *)


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



