A339279 Number of partitions of 3*n into powers of 3 where every part appears at least 2 times.
1, 1, 2, 3, 4, 5, 7, 8, 10, 13, 15, 18, 22, 25, 29, 34, 38, 43, 50, 55, 62, 70, 77, 85, 95, 103, 113, 126, 136, 149, 164, 177, 192, 210, 225, 243, 265, 283, 305, 330, 352, 377, 406, 431, 460, 494, 523, 557, 595, 629, 667, 710, 748, 791, 841, 884, 934, 989, 1039, 1094, 1156
Offset: 0
Keywords
Examples
a(3) = 3 because we have [3, 3, 3], [3, 3, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1].
Programs
Formula
G.f.: (1/(1 - x^2)) * Product_{k>=0} 1/(1 - x^(3^k)).
G.f.: (1/(1 - x)) * Product_{k>=0} (1 + x^(2*3^k)/(1 - x^(3^k))).
a(n) = [x^(3*n)] Product_{k>=0} (1 + x^(2*3^k)/(1 - x^(3^k))).
a(n) = Sum_{k=0..n} (-1)^(n-k) * A005704(k).