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G.f. A(x) satisfies A(x) = 1 / (1 - x * (1 + x + x^2 + x^3) * A(x^4)).
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%I #9 Nov 26 2023 08:38:05

%S 1,1,2,4,8,16,32,64,128,257,515,1032,2068,4146,8310,16656,33384,66916,

%T 134125,268837,538850,1080064,2164860,4339204,8697416,17432944,

%U 34942268,70037629,140382111,281379296,563991416,1130453878,2265860666,4541648896,9103196384

%N G.f. A(x) satisfies A(x) = 1 / (1 - x * (1 + x + x^2 + x^3) * A(x^4)).

%F a(0) = 1; a(n) = Sum_{k=0..n-1} a(floor(k/4)) * a(n-1-k).

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, v[j\4+1]*v[i-j])); v;

%Y Cf. A127680, A367652, A367654.

%Y Cf. A367660.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 26 2023