Number of subsets of {1..n} containing n and some element equal to the sum of two distinct others.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =2a(5) =7a(6) =17a(7) =40a(8) =87a(9) =196a(10) =413a(11) =875a(12) =1812a(13) =3741a(14) =7640a(15) =15567a(16) =31493a(17) =63666a(18) =128284a(19) =257977a(20) =518045a(21) =1039478a(22) =2083719a(23) =4174586a(24) =8359837a(25) =16735079a(26) =33493780a(27) =67020261a(28) =134090173a(29) =268250256