OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..40
FORMULA
The partitions of 2*3^n into powers of 3, or, the coefficient of x^(2*3^n) in 1/Product_{j=0..inf}(1-x^(3^j)) (conjecture).
EXAMPLE
a(1)=3 since the coefficient of x^6 in 1/Product_{j=0..inf}(1-x^(3^j)) = 1 + x + x^2 + 2x^3 + 2x^4 + 2x^5 + 3x^6 + ... is 3.
MATHEMATICA
m[i_, j_] := m[i, j]=If[j==0||i==j, 1, m3[i-1, j-1]]; m2[i_, j_] := m2[i, j]=Sum[m[i, k]m[k, j], {k, j, i}]; m3[i_, j_] := m3[i, j]=Sum[m[i, k]m2[k, j], {k, j, i}]; a[n_] := m[n+1, 1]
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 18 2002
STATUS
approved