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A020990
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a(n) = Sum_{k=0..n} (-1)^k*A020985(k).
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1
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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)
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OFFSET
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0,4
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LINKS
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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.
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FORMULA
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Brillhart and Morton (1978) list many properties.
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PROG
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(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
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CROSSREFS
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Cf. A033999.
Sequence in context: A165592 A059285 A165578 * A260686 A037891 A037899
Adjacent sequences: A020987 A020988 A020989 * A020991 A020992 A020993
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KEYWORD
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nonn,changed
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Edited by N. J. A. Sloane, Jun 06 2012
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STATUS
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approved
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