Total number of elements (with multiplicity) in all subsets of [n] having a square element sum.

Terms

a(0) =0a(1) =1a(2) =1a(3) =3a(4) =7a(5) =12a(6) =30a(7) =61a(8) =124a(9) =247a(10) =491a(11) =980a(12) =1962a(13) =3949a(14) =7916a(15) =15863a(16) =31815a(17) =63692a(18) =127570a(19) =255529a(20) =511627a(21) =1024421a(22) =2051038a(23) =4105848a(24) =8218842a(25) =16450989a(26) =32926094a(27) =65897438a(28) =131879440a(29) =263915641