Number of length 1+3 0..n arrays with no pair in any consecutive four terms totalling exactly n.

Terms

a(0) =2a(1) =10a(2) =60a(3) =172a(4) =462a(5) =966a(6) =1880a(7) =3256a(8) =5370a(9) =8290a(10) =12372a(11) =17700a(12) =24710a(13) =33502a(14) =44592a(15) =58096a(16) =74610a(17) =94266a(18) =117740a(19) =145180a(20) =177342a(21) =214390a(22) =257160a(23) =305832a(24) =361322a(25) =423826a(26) =494340a(27) =573076a(28) =661110a(29) =758670