Number of length 1+2 0..n arrays with no pair in any consecutive three terms totaling exactly n.

Terms

a(0) =2a(1) =8a(2) =28a(3) =64a(4) =126a(5) =216a(6) =344a(7) =512a(8) =730a(9) =1000a(10) =1332a(11) =1728a(12) =2198a(13) =2744a(14) =3376a(15) =4096a(16) =4914a(17) =5832a(18) =6860a(19) =8000a(20) =9262a(21) =10648a(22) =12168a(23) =13824a(24) =15626a(25) =17576a(26) =19684a(27) =21952a(28) =24390a(29) =27000