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%I #18 Mar 01 2022 12:01:39
%S 1,-1,1,-1,1,-1,1,0,-1,2,-3,4,-5,5,-4,2,1,-5,10,-15,19,-21,20,-15,5,
%T 10,-29,50,-70,85,-90,80,-51,1,69,-154,244,-324,375,-376,307,-153,-91,
%U 414,-788,1163,-1469,1621,-1529,1115,-328,-833,2299,-3916,5440,-6550,6874,-6039,3741,170,-5600,12135,-18990,25008
%N G.f. satisfies: A(x) = 1/(1 + x*A(x^6)) and also the continued fraction: 1+x*A(x^7) = [1;1/x,1/x^6,1/x^36,1/x^216,...,1/x^(6^(n-1)),...].
%C 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
%F a(0) = 1; a(n) = -Sum_{k=0..floor((n-1)/6)} a(k) * a(n-6*k-1). - _Ilya Gutkovskiy_, Mar 01 2022
%p 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
%o (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)
%o (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)
%Y Cf. A101912-A101915, A101917-A101918.
%K sign
%O 0,10
%A _Paul D. Hanna_, Dec 20 2004
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