OFFSET
0,5
FORMULA
From Joerg Arndt, Oct 15 2011: (Start)
For the sequence abs(a(n)) we have
g.f. B(x) 1/(1-x/(1-x^3/(1-x^9/(1-x^27(1- ... ))))) and
B(x) satisfies B(x) = 1 + x*B(x)*B(x^3) (cf. A000621)
(End)
G.f.: T(0), where T(k) = 1 - (-x)^(3^k)/((-x)^(3^k) - 1/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Oct 18 2013
a(0) = 1; a(n) = -Sum_{k=0..floor((n-1)/3)} a(k) * a(n-3*k-1). - Ilya Gutkovskiy, Mar 01 2022
PROG
(PARI) {a(n)=local(A); A=1-x; for(i=1, n\3+1, A=1/(1+x*subst(A, x, x^3)+x*O(x^n))); polcoeff(A, n, x)}
(PARI) {a(n)=local(M=contfracpnqn(concat(1, vector(ceil(log(n+1)/log(3))+1, n, 1/x^(3^(n-1)))))); polcoeff(M[1, 1]/M[2, 1]+x*O(x^(4*n+1)), 4*n+1)}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Dec 20 2004
STATUS
approved