OFFSET
0,3
COMMENTS
LINKS
Paul Barry, Conjectures and results on some generalized Rueppel sequences, arXiv:2107.00442 [math.CO], 2021.
FORMULA
G.f. (1-x+3*x^2+x^3)/(1+x^2) - 2*Sum_{k>=1} x^(3*2^(k-1))/Product_{j=0..k} (1+x^(2^j)).
EXAMPLE
1 + 1/x + 1/x^2 + 1/x^4 + 1/x^8 + 1/x^16 + ... =
[1; x - 1, x + 2, x, x, x - 2, x, x + 2, x, x - 2, ...].
PROG
(PARI) contfrac(1+sum(n=0, 10, 1/x^(2^n)))
(PARI) a(n)=polcoeff((1-x+3*x^2+x^3)/(1+x^2)- 2*sum(k=1, #binary(n), x^(3*2^(k-1))/prod(j=0, k, 1+x^(2^j)+x*O(x^n))), n)
(PARI) a(n)=subst(contfrac(1+sum(k=0, #binary(n+1), 1/x^(2^k)))[n+1], x, 0)
CROSSREFS
KEYWORD
cofr,sign
AUTHOR
Paul D. Hanna, Jul 08 2005
STATUS
approved