A317542 Formal inverse of the period-doubling sequence A096268.

0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0

Offset

0

Links

Manon Stipulanti, Table of n, a(n) for n = 0..10000

N. Rampersad and M. Stipulanti, The Formal Inverse of the Period-Doubling Sequence, arXiv preprint arXiv:1807.11899 [math.CO], 2018.

Formula

a(2n) = 0 for all n >= 0; a(1) = 1, a(4n+1) = a(2n-1) for all n >= 1; a(4n+3) = a(n) for all n >= 0.

Mathematica

a[0] = 0; a[1] = 1; a[2] = 0; a[3] = 0;
a[n_] := If[EvenQ[n], 0,
  If[IntegerQ[(n - 1)/4], a[2 ((n - 1)/4) - 1], a[(n - 3)/4]]]

Prog

(PARI) seq(n)={Vec(lift(serreverse(sum(i=1, n, (valuation(i+1, 2)%2 + O(2))*x^i) + O(x*x^n))), -(n+1))} \\ Andrew Howroyd, Jul 31 2018

Crossrefs

Cf. A096268, A317543, A317544.

Sequence in context: A324772 A285949 A285530 * A322796 A109017 A110161

Adjacent sequences: A317539 A317540 A317541 * A317543 A317544 A317545

Keyword

nonn

Author

Manon Stipulanti, Jul 30 2018

Status

approved