A195261 G.f.: A(x) = 1 + Sum_{n>=1} x^n*A(x)^A000069(n), where A000069 lists numbers with an odd number of 1's in their binary expansion.

1, 1, 3, 12, 56, 284, 1520, 8449, 48303, 282207, 1677489, 10112546, 61678702, 379919672, 2359991520, 14767164162, 92993252612, 588904075546, 3748029131834, 23960546501520, 153790930664222, 990690415079898, 6402865318618654, 41506375396111624

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 56*x^4 + 284*x^5 + 1520*x^6 +...
where
A(x) = 1 + x*A(x) + x^2*A(x)^2 + x^3*A(x)^4 + x^4*A(x)^7 + x^5*A(x)^8 + x^6*A(x)^11 + x^7*A(x)^13 + x^8*A(x)^14 +...
and exponents A000069(n) begin:
[1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,...].

Prog

(PARI) {A000069(n)=2*n+1-subst(Pol(binary(n)), x, 1)%2}
{a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*A^A000069(j))); polcoeff(A, n)}

Crossrefs

Cf. A000069 (odious numbers), A195262.

Sequence in context: A350482 A120921 A226316 * A276902 A192132 A179486

Adjacent sequences: A195258 A195259 A195260 * A195262 A195263 A195264

Keyword

nonn

Author

Paul D. Hanna, Sep 13 2011

Status

approved