OFFSET
0,10
COMMENTS
This sequence resembles the series expansion of B(x) = (1+x^6)/(1+x+x^6). The first difference occurs at a(43) = 415 versus a(43) = 414. - Johannes W. Meijer, Aug 08 2011
FORMULA
a(0) = 1; a(n) = -Sum_{k=0..floor((n-1)/6)} a(k) * a(n-6*k-1). - Ilya Gutkovskiy, Mar 01 2022
MAPLE
nmax:=63: kmax:=nmax: for k from 0 to kmax do A:= proc(x): add(a(n)*x^n, n=0..k) end: f(x):=series(1/(1 + x*A(x^6)), x, k+1); for n from 0 to k do x(n):=coeff(f(x), x, n) od: a(k):=x(k): od: seq(a(n), n=0..nmax); # Johannes W. Meijer, Aug 08 2011
PROG
(PARI) a(n)=local(A); A=1-x; for(i=1, n\6+1, A=1/(1+x*subst(A, x, x^6)+x*O(x^n))); polcoeff(A, n, x)
(PARI) a(n)=local(M=contfracpnqn(concat(1, vector(ceil(log(n+1)/log(6))+1, n, 1/x^(6^(n-1)))))); polcoeff(M[1, 1]/M[2, 1]+x*O(x^(7*n+1)), 7*n+1)
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Dec 20 2004
STATUS
approved