A108804 - OEIS

A108804

Self-convolution of A010060 (Thue-Morse sequence).

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

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OFFSET

0,4

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

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

(SageMath) [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. A010060, A108805.

Cf. A247303.

Sequence in context: A008441 A253183 A391883 * A284467 A200227 A316230

Adjacent sequences: A108801 A108802 A108803 * A108805 A108806 A108807

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 09 2005

STATUS

approved