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

Terms

a(0) =1a(1) =1a(2) =5a(3) =19a(4) =59a(5) =150a(6) =349a(7) =745a(8) =1515a(9) =2936a(10) =5514a(11) =10036a(12) =17851a(13) =31039a(14) =53006a(15) =88943a(16) =147057a(17) =239701a(18) =385885a(19) =613855a(20) =966137a(21) =1505137a(22) =2323124a(23) =3553914a(24) =5392315a(25) =8117758a(26) =12131618a(27) =18003740a(28) =26543030a(29) =38886999