Sum of terms in periodic part of continued fraction expansion of square root of -1+2^n.

Terms

a(0) =0a(1) =3a(2) =7a(3) =7a(4) =25a(5) =15a(6) =63a(7) =31a(8) =125a(9) =63a(10) =187a(11) =127a(12) =1081a(13) =255a(14) =1091a(15) =511a(16) =1247a(17) =1023a(18) =11217a(19) =2047a(20) =11999a(21) =4095a(22) =20259a(23) =8191a(24) =66077a(25) =16383a(26) =88609a(27) =32767a(28) =55491a(29) =65535