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A185202 G.f. A(x) satisfies: x = Sum_{n>=0} -(-A(x))^A000069(n), where A000069 is the odious numbers. 0
1, 1, 2, 6, 20, 70, 255, 961, 3717, 14663, 58758, 238524, 978844, 4054152, 16924986, 71145392, 300876074, 1279225578, 5464762332, 23444755016, 100968932096, 436355661280, 1891770895672, 8225329914410, 35858439130786, 156708088823482, 686392551655052 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
The odious numbers (A000069) have an odd number of 1's in their binary expansion.
LINKS
FORMULA
Equals the series reversion of the g.f. of the Thue-Morse sequence (A010060) evaluated at x = -x.
EXAMPLE
G.f.: A(x) = x + x^2 + 2*x^3 + 6*x^4 + 20*x^5 + 70*x^6 + 255*x^7 +...
Series reversion of the g.f. yields:
G(x) = x - x^2 - x^4 + x^7 - x^8 + x^11 + x^13 - x^14 - x^16 + x^19 + x^21 - x^22 + x^25 +..+ -(-x)^A000069(n) +...
PROG
(PARI) {odious(n)=if(n==0, 1, if(n%2==0, odious(n/2)+n, -odious((n-1)/2)+3*n))}
{a(n)=polcoeff(serreverse(sum(k=1, n+1, -(-x)^odious(k-1)+x^2*O(x^n))), n)}
CROSSREFS
Cf. A000069 (odious numbers), A010060 (Thue-Morse).
Sequence in context: A049128 A192540 A369630 * A340891 A049140 A092413
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 24 2012
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)