A Graham-Pollak-like sequence with multiplier 3 instead of 2.

Terms

a(0) =1a(1) =2a(2) =4a(3) =7a(4) =12a(5) =21a(6) =37a(7) =64a(8) =111a(9) =193a(10) =335a(11) =581a(12) =1007a(13) =1745a(14) =3023a(15) =5236a(16) =9069a(17) =15708a(18) =27207a(19) =47124a(20) =81622a(21) =141374a(22) =244867a(23) =424122a(24) =734601a(25) =1272367a(26) =2203805a(27) =3817103a(28) =6611417a(29) =11451311