A393313 G.f. A(x) satisfies: A(x) = (1 + x + x^2)^2 * A(x^3) / (1 - x).

1, 3, 6, 11, 18, 27, 39, 54, 72, 95, 123, 156, 196, 243, 297, 360, 432, 513, 606, 711, 828, 960, 1107, 1269, 1449, 1647, 1863, 2102, 2364, 2649, 2962, 3303, 3672, 4074, 4509, 4977, 5485, 6033, 6621, 7256, 7938, 8667, 9450, 10287, 11178, 12132, 13149, 14229, 15381, 16605, 17901

Offset

0,2

Links

Table of n, a(n) for n=0..50.

Formula

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

a(n) = a(n-3) + a(floor(n/3)) + 2 * a(floor((n-1)/3)) + 3 * a(floor((n-2)/3)) + 2 * a(floor((n-3)/3)) + a(floor((n-4)/3)) for n > 3.

Mathematica

nmax = 50; A[_] = 1; Do[A[x_] = (1 + x + x^2)^2 A[x^3]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
nmax = 50; CoefficientList[Series[1/(1 - x)^2 Product[1/(1 - x^(3^k)), {k, 0, Floor[Log[3, nmax]] + 1}], {x, 0, nmax}], x]

Crossrefs

Partial sums of A005704.

Cf. A062051, A131205, A393314.

Sequence in context: A183199 A172046 A014125 * A147456 A230088 A011849

Adjacent sequences: A393310 A393311 A393312 * A393314 A393315 A393316

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 10 2026

Status

approved