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A108804 Self-convolution of A010060 (Thue-Morse sequence). 3
0, 0, 1, 2, 1, 2, 2, 0, 3, 4, 2, 2, 4, 2, 3, 8, 3, 4, 6, 2, 6, 6, 5, 8, 6, 4, 7, 10, 5, 10, 10, 0, 11, 12, 6, 10, 10, 6, 9, 16, 8, 8, 13, 10, 11, 14, 12, 8, 14, 12, 11, 18, 11, 14, 16, 8, 15, 20, 14, 10, 20, 10, 11, 32, 11, 12, 22, 10, 18, 22, 17, 16, 20, 16, 17, 26, 15, 22, 24, 8, 24, 24, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
a(2n+1) = (1/2) * (A115384(n) - 2a(n)). - Ralf Stephan, Aug 23 2013
G.f.: (1/4)*(1/(1 - x) - Product_{k>=0} (1 - x^(2^k)))^2. - Ilya Gutkovskiy, Apr 03 2019
a(n) = Sum_{k=0..n} A010060(k)*A010060(n-k), for n>=0. - G. C. Greubel, Apr 03 2019
MATHEMATICA
Table[Sum[ThueMorse[k]*ThueMorse[n-k], {k, 0, n}], {n, 0, 85}] (* G. C. Greubel, Apr 03 2019 *)
PROG
(PARI) a(n)=sum(k=0, n, (subst(Pol(binary(k)), x, 1)%2)*(subst(Pol(binary(n-k)), x, 1)%2)) /* Ralf Stephan, Aug 23 2013 */
(PARI) {a(n)=sum(k=0, n, (hammingweight(k)*hammingweight(n-k))%2)};
vector(85, n, n--; a(n)) \\ G. C. Greubel, Apr 03 2019
(Haskell)
a108804 n = a108804_list !! n
a108804_list = f [head a010060_list] $ tail a010060_list where
f xs (z:zs) = (sum $ zipWith (*) xs (reverse xs)) : f (z : xs) zs
-- Reinhard Zumkeller, Sep 14 2014
(Sage) [sum(sloane.A010060(k)*sloane.A010060(n-k) for k in (0..n)) for n in (0..85)] # G. C. Greubel, Apr 03 2019
CROSSREFS
Cf. A247303.
Sequence in context: A134343 A008441 A253183 * A284467 A200227 A316230
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 09 2005
STATUS
approved

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)