%I #9 Nov 28 2023 08:51:00
%S 1,0,2,2,6,9,20,36,72,138,269,520,1010,1958,3798,7365,14284,27704,
%T 53728,104202,202089,391939,760128,1474208,2859096,5544986,10754022,
%U 20856528,40449464,78448346,152143931,295070345,572264028,1109857872,2152475724,4174545216
%N G.f. A(x) satisfies A(x) = 1 / ((1 + x) * (1 - x * (1 + x + x^2 + x^3) * A(x^4))).
%F a(n) = (-1)^n + Sum_{k=0..n-1} a(floor(k/4)) * 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\4+1]*v[i-j])); v;
%Y Cf. A005043, A367716, A367717.
%Y Cf. A367694, A367715.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 28 2023