OFFSET
1,2
COMMENTS
Self-convolution of the signed Thue-Morse sequence A106400. - Vladimir Reshetnikov, Apr 13 2018
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
Maciej Gawron, Piotr Miska, Maciej Ulas, Arithmetic properties of coefficients of power series expansion of Prod_{n>=0} (1-x^(2^n))^t, arXiv:1703.01955 [math.NT], 2017.
Eric Rowland, A matrix generalization of a theorem of Fine, arXiv:1704.05872 [math.NT], 2017.
Eric Rowland, A matrix generalization of a theorem of Fine, Integers, Electronic Journal of Combinatorial Number Theory 18A (2018), #A18.
FORMULA
Euler transform of sequence b(n) where b(2^k)=-2 and zero otherwise.
G.f.: A(x) satisfies 0=f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6)=u1^3*u6 + 6*u1^2*u2*u6 + 9*u1*u2^2*u6 - u3*u2^3.
G.f.: x(Product_{k>=0} (1-x^(2^k)))^2.
G.f.: A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)=-v^3+4uvw+u^2w.
MATHEMATICA
Table[Sum[(-1)^(DigitCount[k, 2, 1] + DigitCount[n-k-1, 2, 1]), {k, 0, n-1}], {n, 1, 80}] (* Vladimir Reshetnikov, Apr 13 2018 *)
PROG
(PARI) {a(n)=local(A, m); if(n<1, 0, n--; A=1+x*O(x^n); m=1; while(m<=n, A*=(1-x^m); m*=2; ); polcoeff(A^2, n))}
CROSSREFS
KEYWORD
sign,look
AUTHOR
Michael Somos, May 02 2005
STATUS
approved