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

%I #11 Jul 29 2023 10:48:24

%S 1,1,1,1,2,4,7,11,19,37,74,142,268,518,1033,2077,4152,8290,16687,

%T 33899,69148,141160,288650,592354,1220086,2519226,5210164,10794088,

%U 22408556,46613554,97125751,202662419,423459427,886048249,1856448852,3894362560,8178530890

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

%F a(n) = Sum_{k=0..floor(n/4)} binomial(n-2*k,2*k) * binomial(3*k,k) / (2*k+1).

%o (PARI) a(n) = sum(k=0, n\4, binomial(n-2*k, 2*k)*binomial(3*k, k)/(2*k+1));

%Y Cf. A346073, A364591.

%Y Cf. A049130, A199475, A364589.

%K nonn,easy

%O 0,5

%A _Seiichi Manyama_, Jul 29 2023