Number of nonempty subsets of {1,2,...,n} in which exactly 1/3 of the elements are <= (n-3)/3.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =10a(6) =15a(7) =21a(8) =77a(9) =126a(10) =198a(11) =570a(12) =975a(13) =1617a(14) =4213a(15) =7425a(16) =12753a(17) =31421a(18) =56511a(19) =99403a(20) =236203a(21) =431098a(22) =771562a(23) =1787346a(24) =3298527a(25) =5981865a(26) =13598053a(27) =25314061a(28) =46385069a(29) =103918153