OFFSET
0,2
COMMENTS
The Hankel transforms of Phi(x) and Phi(x^2) are identical. See Theorem 2.8 in Han paper.
LINKS
Michel Marcus, Table of n, a(n) for n = 0..1000
Guo-Niu Han, Jacobi continued fraction and Hankel determinants of the Thue-Morse sequence, Quaestiones Mathematicae, 2016, 39 (7), pp.895-909. hal-02125285.
FORMULA
MATHEMATICA
a[n_] := Sum[(-1)^(n - k) * Binomial[n, k] * (-1)^(2*n - 2*k + DigitCount[k, 2, 1]), {k, 0, n}]; Array[a, 36, 0] (* Amiram Eldar, May 16 2020 *)
PROG
(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*(-1)^(2*n-2*k+hammingweight(k)));
CROSSREFS
KEYWORD
sign
AUTHOR
Michel Marcus, May 16 2020
STATUS
approved