login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A020986 a(n) = n-th partial sum of Golay-Rudin-Shapiro sequence A020985. 13
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
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.
Narad Rampersad and Jeffrey Shallit, Rudin-Shapiro Sums Via Automata Theory and Logic, arXiv:2302.00405 [math.NT], February 1 2023.
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 *)
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
(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
CROSSREFS
Sequence in context: A363678 A194960 A111439 * A326820 A095161 A072106
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
Minor edits by N. J. A. Sloane, Jun 06 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:09 EDT 2024. Contains 370951 sequences. (Running on oeis4.)