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G.f. A(x) satisfies A(x) = 1 / ((1 + x) * (1 - x * (1 + x + x^2) * A(x^3))).
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%I #9 Nov 28 2023 08:50:56

%S 1,0,2,2,5,8,16,30,57,108,206,390,741,1407,2670,5068,9622,18262,34666,

%T 65806,124911,237109,450092,854368,1621784,3078519,5843709,11092672,

%U 21056400,39969753,75871567,144021302,273384733,518945611,985075356,1869894158,3549478993

%N G.f. A(x) satisfies A(x) = 1 / ((1 + x) * (1 - x * (1 + x + x^2) * A(x^3))).

%F a(n) = (-1)^n + Sum_{k=0..n-1} a(floor(k/3)) * a(n-1-k).

%o (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-1)^i+sum(j=0, i-1, v[j\3+1]*v[i-j])); v;

%Y Cf. A005043, A367716, A367718.

%Y Cf. A367693, A367714.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 28 2023