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 A317542 Formal inverse of the period-doubling sequence A096268. 3

%I

%S 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,

%T 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,

%U 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

%N Formal inverse of the period-doubling sequence A096268.

%H Manon Stipulanti, <a href="/A317542/b317542.txt">Table of n, a(n) for n = 0..10000</a>

%H N. Rampersad and M. Stipulanti, <a href="https://arxiv.org/abs/1807.11899">The Formal Inverse of the Period-Doubling Sequence</a>, arXiv preprint arXiv:1807.11899 [math.CO], 2018.

%F 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.

%t a[0] = 0; a[1] = 1; a[2] = 0; a[3] = 0;

%t a[n_] := If[EvenQ[n], 0,

%t If[IntegerQ[(n - 1)/4], a[2 ((n - 1)/4) - 1], a[(n - 3)/4]]]

%o (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

%Y Cf. A096268, A317543, A317544.

%K nonn

%O 0

%A _Manon Stipulanti_, Jul 30 2018

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Last modified October 17 11:26 EDT 2019. Contains 328108 sequences. (Running on oeis4.)