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A317542 Formal inverse of the period-doubling sequence A096268. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 22 20:38 EDT 2019. Contains 326186 sequences. (Running on oeis4.)