Difference between maximum and minimum sum of products of successive pairs in permutations of [n].

Terms

a(0) =0a(1) =0a(2) =0a(3) =4a(4) =11a(5) =24a(6) =42a(7) =68a(8) =101a(9) =144a(10) =196a(11) =260a(12) =335a(13) =424a(14) =526a(15) =644a(16) =777a(17) =928a(18) =1096a(19) =1284a(20) =1491a(21) =1720a(22) =1970a(23) =2244a(24) =2541a(25) =2864a(26) =3212a(27) =3588a(28) =3991a(29) =4424