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%I #11 Jul 29 2023 10:55:13
%S 1,1,1,2,4,7,15,36,82,191,471,1166,2884,7267,18523,47349,121821,
%T 315781,822165,2148811,5641035,14864295,39287907,104154066,276899112,
%U 737984583,1971375679,5277570860,14156881590,38045460023,102421374775,276174537027,745822179831
%N G.f. satisfies A(x) = 1/(1-x) + x^3*(1-x)*A(x)^4.
%F a(n) = Sum_{k=0..floor(n/3)} binomial(n-k,2*k) * binomial(4*k,k) / (3*k+1).
%o (PARI) a(n) = sum(k=0, n\3, binomial(n-k, 2*k)*binomial(4*k, k)/(3*k+1));
%Y Cf. A364595, A364597.
%Y Cf. A215340, A226974.
%Y Cf. A364592, A364594.
%K nonn,easy
%O 0,4
%A _Seiichi Manyama_, Jul 29 2023
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