A393316 G.f. A(x) satisfies: A(x) = A(x^3) / (1 - x - x^2 - x^3).

1, 1, 2, 5, 8, 15, 30, 53, 98, 186, 337, 621, 1152, 2110, 3883, 7160, 13153, 24196, 44539, 81888, 150623, 277103, 509614, 937340, 1724155, 3171109, 5832604, 10728054, 19731767, 36292425, 66752583, 122776775, 225821783, 415351762, 763950320, 1405123865, 2584427099

Offset

0,3

Links

Table of n, a(n) for n=0..36.

Formula

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

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

Mathematica

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]
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]

Crossrefs

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

Sequence in context: A081660 A285291 A065618 * A257548 A186413 A080084

Adjacent sequences: A393313 A393314 A393315 * A393317 A393318 A393319

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 10 2026

Status

approved