Number of length 1+4 0..n arrays with no pair in any consecutive five terms totalling exactly n.

Terms

a(0) =2a(1) =12a(2) =124a(3) =424a(4) =1566a(5) =3876a(6) =9368a(7) =18768a(8) =36250a(9) =63100a(10) =106452a(11) =168312a(12) =259574a(13) =383124a(14) =554416a(15) =777376a(16) =1072818a(17) =1445868a(18) =1923500a(19) =2512200a(20) =3245902a(21) =4132612a(22) =5214024a(23) =6499824a(24) =8040266a(25) =9846876a(26) =11979268a(27) =14450968a(28) =17331750a(29) =20637300