a(n) = a(n-1) + a(floor(n/2))^2 for n > 0, a(0) = 1.

Terms

a(0) =1a(1) =2a(2) =6a(3) =10a(4) =46a(5) =82a(6) =182a(7) =282a(8) =2398a(9) =4514a(10) =11238a(11) =17962a(12) =51086a(13) =84210a(14) =163734a(15) =243258a(16) =5993662a(17) =11744066a(18) =32120262a(19) =52496458a(20) =178789102a(21) =305081746a(22) =627715190a(23) =950348634a(24) =3560128030a(25) =6169907426a(26) =13261231526a(27) =20352555626a(28) =47161378382a(29) =73970201138