A393316 - OEIS

%I #4 Feb 15 2026 22:59:28

%S 1,1,2,5,8,15,30,53,98,186,337,621,1152,2110,3883,7160,13153,24196,

%T 44539,81888,150623,277103,509614,937340,1724155,3171109,5832604,

%U 10728054,19731767,36292425,66752583,122776775,225821783,415351762,763950320,1405123865,2584427099

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

%F G.f.: Product_{k>=0} 1 / (1 - x^(3^k) - x^(2*3^k) - x^(3^(k+1))).

%F a(0) = 1; a(n) = Sum_{k=0..floor(n/3)} A000073(n-3*k+2) * a(k).

%t nmax = 36; A[_] = 1; Do[A[x_] =  A[x^3]/(1 - x - x^2 - x^3) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

%t nmax = 36; CoefficientList[Series[Product[1/(1 - x^(3^k) - x^(2 3^k) - x^(3^(k+1))), {k, 0, Floor[Log[3, nmax]] + 1}], {x, 0, nmax}], x]

%Y Cf. A000073, A054390, A062051, A309702, A345007, A393315.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Feb 10 2026