Number of compositions of n with c(1) = 1, c(i+1) - c(i) <= 1, and c(i+1) - c(i) != 0.

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =1a(5) =0a(6) =2a(7) =2a(8) =1a(9) =4a(10) =4a(11) =4a(12) =9a(13) =10a(14) =11a(15) =21a(16) =25a(17) =30a(18) =51a(19) =62a(20) =80a(21) =125a(22) =157a(23) =208a(24) =309a(25) =399a(26) =536a(27) =772a(28) =1013a(29) =1373