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

Terms

a(0) =3a(1) =4a(2) =0a(3) =8a(4) =14a(5) =16a(6) =42a(7) =32a(8) =82a(9) =64a(10) =270a(11) =128a(12) =518a(13) =256a(14) =642a(15) =512a(16) =2126a(17) =1024a(18) =7098a(19) =2048a(20) =7502a(21) =4096a(22) =14550a(23) =8192a(24) =19810a(25) =16384a(26) =108802a(27) =32768a(28) =101154a(29) =65536