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

Terms

a(0) =10a(1) =14a(2) =20a(3) =28a(4) =38a(5) =52a(6) =72a(7) =100a(8) =138a(9) =190a(10) =262a(11) =362a(12) =500a(13) =690a(14) =952a(15) =1314a(16) =1814a(17) =2504a(18) =3456a(19) =4770a(20) =6584a(21) =9088a(22) =12544a(23) =17314a(24) =23898a(25) =32986a(26) =45530a(27) =62844a(28) =86742a(29) =119728