a(n) = [2^n/(1 - cos(1/n))] - [2^n/(-1 + cot(1/n))], where [ ] = floor.

Terms

a(0) =10a(1) =28a(2) =141a(3) =509a(4) =1597a(5) =4606a(6) =12544a(7) =32774a(8) =82965a(9) =204856a(10) =495752a(11) =1179957a(12) =2769577a(13) =6423997a(14) =14748718a(15) =33560981a(16) =75773263a(17) =169897572a(18) =378594174a(19) =838980348a(20) =1849932688a(21) =4060585522a(22) =8876163946a(23) =19329419393a(24) =41947233974a(25) =90739684034a(26) =195706653907a(27) =420941590665