a(n) = Sum_{k=0..floor(n/2)} binomial(2*n-k,3*k).

Terms

a(0) =1a(1) =1a(2) =2a(3) =11a(4) =37a(5) =113a(6) =377a(7) =1266a(8) =4175a(9) =13785a(10) =45665a(11) =151169a(12) =500162a(13) =1655187a(14) =5477917a(15) =18128529a(16) =59993817a(17) =198543154a(18) =657057431a(19) =2174457329a(20) =7196122817a(21) =23814769985a(22) =78812331010a(23) =260820625435a(24) =863156812373