A185202 G.f. A(x) satisfies: x = Sum_{n>=0} -(-A(x))^A000069(n), where A000069 is the odious numbers.

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

Offset

1,3

Comments

The odious numbers (A000069) have an odd number of 1's in their binary expansion.

Links

Table of n, a(n) for n=1..27.

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 A372526

Adjacent sequences: A185199 A185200 A185201 * A185203 A185204 A185205

Keyword

nonn

Author

Paul D. Hanna, Jan 24 2012

Status

approved