a(n) = Sum_{k=0..n} S(k), where S(n) are the tribonacci generalized numbers A001644.

Terms

a(0) =3a(1) =4a(2) =7a(3) =14a(4) =25a(5) =46a(6) =85a(7) =156a(8) =287a(9) =528a(10) =971a(11) =1786a(12) =3285a(13) =6042a(14) =11113a(15) =20440a(16) =37595a(17) =69148a(18) =127183a(19) =233926a(20) =430257a(21) =791366a(22) =1455549a(23) =2677172a(24) =4924087a(25) =9056808a(26) =16658067a(27) =30638962a(28) =56353837a(29) =103650866