a(n) = 2^(n+1) - n - 2, or partial sums of main diagonal of array A125127 of k-step Lucas numbers.

Terms

a(0) =1a(1) =4a(2) =11a(3) =26a(4) =57a(5) =120a(6) =247a(7) =502a(8) =1013a(9) =2036a(10) =4083a(11) =8178a(12) =16369a(13) =32752a(14) =65519a(15) =131054a(16) =262125a(17) =524268a(18) =1048555a(19) =2097130a(20) =4194281a(21) =8388584a(22) =16777191a(23) =33554406a(24) =67108837a(25) =134217700a(26) =268435427a(27) =536870882a(28) =1073741793a(29) =2147483616