Index position of {n}^3 within the list of partitions of 3n in canonical ordering.

Terms

a(0) =1a(1) =3a(2) =8a(3) =19a(4) =44a(5) =93a(6) =187a(7) =357a(8) =657a(9) =1166a(10) =2015a(11) =3393a(12) =5594a(13) =9044a(14) =14378a(15) =22501a(16) =34734a(17) =52931a(18) =79735a(19) =118823a(20) =175337a(21) =256347a(22) =371606a(23) =534377a(24) =762721a(25) =1080979a(26) =1521925a(27) =2129330a(28) =2961580a(29) =4096006