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A020990 a(n) = Sum_{k=0..n} (-1)^k*A020985(k). 1
1, 0, 1, 2, 3, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 4, 5, 4, 5, 6, 7, 6, 5, 4, 3, 4, 3, 2, 3, 2, 1, 0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 4, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 5, 6, 5, 6, 7, 8, 9, 8, 9, 10, 11, 10, 9, 8, 9, 8, 9, 10, 9, 10, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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). - 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.

FORMULA

Brillhart and Morton (1978) list many properties.

PROG

(Haskell)

a020990 n = a020990_list !! n

a020990_list = scanl1 (+) $ zipWith (*) a033999_list a020985_list

-- Reinhard Zumkeller, Jun 06 2012

(PARI) a(n) = sum(k=0, n, (-1)^(k+hammingweight(bitand(k, k>>1)))); \\ Michel Marcus, Oct 07 2017

CROSSREFS

Cf. A033999.

Sequence in context: A165592 A059285 A165578 * A260686 A037891 A037899

Adjacent sequences:  A020987 A020988 A020989 * A020991 A020992 A020993

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Edited by N. J. A. Sloane, Jun 06 2012

STATUS

approved

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Last modified September 25 15:23 EDT 2018. Contains 315392 sequences. (Running on oeis4.)