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%I #10 Nov 03 2023 11:18:20
%S 1,1,4,21,136,941,6864,52006,405312,3228654,26170764,215166638,
%T 1789998808,15040070843,127450104568,1087988783356,9347556057040,
%U 80766068931498,701359680126592,6117887649100980,53581405635501276,470988258063461393
%N G.f. satisfies A(x) = 1 - x^3 + x*A(x)^4.
%F a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(3*(n-3*k)+1,k) * binomial(4*(n-3*k),n-3*k)/(3*(n-3*k)+1).
%o (PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(3*(n-3*k)+1, k)*binomial(4*(n-3*k), n-3*k)/(3*(n-3*k)+1));
%Y Cf. A226022, A367046.
%Y Cf. A367043.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 03 2023
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