Number of subsets of {1,...,n} containing an arithmetic progression of length 3.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =3a(5) =9a(6) =24a(7) =63a(8) =150a(9) =343a(10) =746a(11) =1605a(12) =3391a(13) =7075a(14) =14624a(15) =30076a(16) =61385a(17) =124758a(18) =252618a(19) =510161a(20) =1027632a(21) =2066304a(22) =4148715a(23) =8322113a(24) =16680369a(25) =33413592a(26) =66904484a(27) =133923906a(28) =268009597a(29) =536257466