Number of compositions of n whose multiplicities cover an initial interval of positive integers.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =6a(5) =11a(6) =14a(7) =34a(8) =52a(9) =114a(10) =225a(11) =464a(12) =539a(13) =1183a(14) =1963a(15) =3753a(16) =6120a(17) =11207a(18) =19808a(19) =38254a(20) =77194a(21) =147906a(22) =224853a(23) =374216a(24) =611081a(25) =1099933a(26) =2129347a(27) =3336099a(28) =5816094a(29) =9797957