A227318 G.f.: Sum_{n>=0} x^n * (1-x)^A007814(n), where A007814(n) is the exponent of the highest power of 2 dividing n.

1, 1, 1, 0, 1, -1, 2, 0, 1, -2, 4, -1, 1, -1, 2, 0, 1, -3, 7, -4, 2, -1, 2, 0, 1, -2, 4, -1, 1, -1, 2, 0, 1, -4, 11, -10, 6, -2, 2, 0, 1, -2, 4, -1, 1, -1, 2, 0, 1, -3, 7, -4, 2, -1, 2, 0, 1, -2, 4, -1, 1, -1, 2, 0, 1, -5, 16, -20, 16, -7, 3, 0, 1, -2, 4, -1, 1, -1, 2, 0, 1, -3, 7, -4, 2, -1, 2, 0, 1, -2, 4, -1, 1, -1, 2, 0, 1, -4, 11, -10, 6, -2, 2, 0, 1, -2, 4, -1, 1, -1, 2, 0, 1, -3, 7, -4, 2, -1, 2, 0, 1, -2, 4, -1, 1, -1, 2, 0, 1

Offset

0,7

Comments

Compare to g.f. of A227277: Sum_{n>=0} x^n*(1+x)^A007814(n).

Links

Paul D. Hanna, Table of n, a(n) for n = 0..10000

Example

G.f.: A(x) = 1 + x + x^2 + x^4 - x^5 + 2*x^6 + x^8 - 2*x^9 + 4*x^10 - x^11 + x^12 - x^13 + 2*x^14 + x^16 - 3*x^17 + 7*x^18 - 4*x^19 + 2*x^20 +...
where
A(x) = 1 + x + x^2*(1-x) + x^3 + x^4*(1-x)^2 + x^5 + x^6*(1-x) + x^7 + x^8*(1-x)^3 + x^9 + x^10*(1-x) + x^11 + x^12*(1-x)^2 + x^13 + x^14*(1-x) + x^16*(1-x)^4 +...

Prog

(PARI) {a(n)=polcoeff(1+sum(m=1, n, x^m*(1-x+x*O(x^n))^valuation(m, 2)), n)}
for(n=0, 128, print1(a(n), ", "))

Crossrefs

Cf. A227277, A227287.

Sequence in context: A264157 A361853 A144172 * A166692 A046766 A292147

Adjacent sequences: A227315 A227316 A227317 * A227319 A227320 A227321

Keyword

sign

Author

Paul D. Hanna, Jul 06 2013

Status

approved