Number of length 2+3 0..n arrays with no pair in any consecutive four terms totalling exactly n.

Terms

a(0) =2a(1) =14a(2) =132a(3) =484a(4) =1734a(5) =4386a(6) =10376a(7) =20840a(8) =39690a(9) =68950a(10) =115212a(11) =181644a(12) =278222a(13) =409514a(14) =589584a(15) =824656a(16) =1133586a(17) =1524510a(18) =2021780a(19) =2635700a(20) =3396822a(21) =4317874a(22) =5436312a(23) =6767544a(24) =8356634a(25) =10221926a(26) =12416796a(27) =14962780a(28) =17922270a(29) =21320250