Number of flat partitions of n: partitions {a_i} with each |a_i - a_{i-1}| <= 1.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =4a(5) =5a(6) =7a(7) =8a(8) =10a(9) =13a(10) =15a(11) =18a(12) =23a(13) =26a(14) =31a(15) =39a(16) =44a(17) =52a(18) =63a(19) =72a(20) =85a(21) =101a(22) =115a(23) =134a(24) =158a(25) =181a(26) =208a(27) =243a(28) =277a(29) =318