A195262 G.f.: A(x) = Sum_{n>=0} x^n*A(x)^A001969(n+1), where A001969 lists numbers with an even number of 1's in their binary expansion.

1, 1, 4, 21, 125, 805, 5459, 38403, 277667, 2050771, 15405655, 117344350, 904175038, 7035182178, 55197856415, 436221495843, 3469249248383, 27744896161177, 222987118478532, 1800106801933350, 14589674016207940, 118674224290447850, 968474133792224994

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Example

G.f.: A(x) = 1 + x + 4*x^2 + 21*x^3 + 125*x^4 + 805*x^5 + 5459*x^6 +...
where
A(x) = 1 + x*A(x)^3 + x^2*A(x)^5 + x^3*A(x)^6 + x^4*A(x)^9 + x^5*A(x)^10 + x^6*A(x)^12 + x^7*A(x)^15 + x^8*A(x)^17 +...
and exponents A001969(n) begin:
[0,3,5,6,9,10,12,15,17,18,20,23,24,27,29,30,33,34,36,39,40,...].

Prog

(PARI) {A000120(n)=n-sum(k=1, #binary(n), floor(n/2^k))}
{A001969(n) = (1/2)*(4*n+1-(-1)^A000120(n))}
{a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*A^A001969(j))); polcoeff(A, n)}

Crossrefs

Cf. A001969 (evil numbers), A195261.

Sequence in context: A093965 A370545 A366115 * A162480 A275758 A003168

Adjacent sequences: A195259 A195260 A195261 * A195263 A195264 A195265

Keyword

nonn

Author

Paul D. Hanna, Sep 13 2011

Status

approved