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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
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
Sequence in context: A324772 A285949 A285530 * A322796 A109017 A110161
KEYWORD
nonn
AUTHOR
Manon Stipulanti, Jul 30 2018
STATUS
approved

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Last modified May 29 11:52 EDT 2024. Contains 372940 sequences. (Running on oeis4.)