A309677 G.f. A(x) satisfies: A(x) = A(x^3) / (1 - x)^2.

1, 2, 3, 6, 9, 12, 18, 24, 30, 42, 54, 66, 87, 108, 129, 162, 195, 228, 279, 330, 381, 456, 531, 606, 711, 816, 921, 1068, 1215, 1362, 1563, 1764, 1965, 2232, 2499, 2766, 3120, 3474, 3828, 4290, 4752, 5214, 5805, 6396, 6987, 7740, 8493, 9246, 10194, 11142

Offset: 0

Author

Ilya Gutkovskiy, Aug 12 2019

Keywords

• nonn

Comments

Self-convolution of A062051.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A005704, A062051, A120880, A171238, A309678, A309679.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<0, 0,
      b(n, i-1)+(p-> `if`(p>n, 0, b(n-p, i)))(3^i)))
    end:
a:= n-> add(b(j, ilog[3](j))*b(n-j, ilog[3](n-j)), j=0..n):
seq(a(n), n=0..52);  # Alois P. Heinz, Aug 12 2019

Mathematica

nmax = 52; A[] = 1; Do[A[x] = A[x^3]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
nmax = 52; CoefficientList[Series[Product[1/(1 - x^(3^k))^2, {k, 0, Floor[Log[3, nmax]] + 1}], {x, 0, nmax}], x]

Formula

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